Active noise control apparatus

[0002] This is a continuation of PCT application Ser. No. PCT/JP99/01984, filed Apr. 14, 1999.

[0003] 1. Field of the Invention

[0004] The present invention relates to an active noise control apparatus, and in particular to an active noise control apparatus for transmitting, from a loud speaker, a secondary noise (pseudo noise) synthesized so as to have the same amplitude as and the opposite phase to a primary noise (noise to be controlled) and to be suppressed small, and for canceling the controlled noise by acoustically overlapping therewith the secondary noise.

[0005] 2. Description of the Related Art

[0006] FIG. 30 shows a prior art example of an active noise control apparatus of a feedforward type. In this example, after a noise flowing through a duct 200 toward an outlet on the right side is detected as a signal x_j(j: sample time index) by a noise detecting microphone 201, the signal x_jis assumed to change into a noise g_jby the time when the signal reaches an error detecting microphone 202.

[0007] In this duration, a noise control filter 220 synthesizes a secondary noise G_jwith the detected noise x_jand a coefficient vector H_jfrom a coefficient updating circuit 240. Obviously when G_j=g_j, the noise is canceled, so that an outputted noise from the outlet of the duct 200 becomes small.

[0008] The coefficient updating circuit 240 updates the coefficient of the noise control filter 220 in order that a signal E_joutputted as a sum of a secondary noise −G_j, to which a phase inversion is performed by multiplying “−1” at a multiplier 205 and which is transmitted from a loud speaker 203, and the noise g_jfrom the error detecting microphone 202 may become a minimum.

[0009] The secondary noise −G_joutputted from the loud speaker 203 feeds back to the noise detecting microphone 201 through the duct 200. At this time, a feedback control filter 210 is inserted in order to intercept the feedback path of the duct 200 leading to the noise detecting microphone 201 from the loud speaker 203 to prevent an occurrence of a howling.

[0010] Also, an error path filter 230 is a filter for simulating a characteristic of an error path leading to the coefficient updating circuit 240 from the output terminal of the multiplier 205 through the loud speaker 203 and the error detecting microphone 202, and is used for a coefficient update of the noise control filter 220.

[0011] At that time, it is necessary for the error path filter 230 to accurately simulate the error path.

[0012] From the structure of the prior art example shown in FIG. 30, it is seen that the noise g_jis canceled when the coefficient of the noise control filter 220 is updated in order that the sum of the secondary noise −G_j, to which the phase inversion is performed at the multiplier 205 and which is transmitted from the loud speaker 203, and the noise g_j, i.e. the output E_jfrom the error detecting microphone 202 may become a minimum. The most typical algorithm applied to the coefficient updating circuit 240 which updates the coefficient vector H_jis a Filtered-x NLMS method applying a general LMS (Least Mean Square) method, which is expressed by the following equation: $\begin{array}{cc}{H}_{j+1}=H_j+\frac{\mu E_j{X}_j}{{\Vert X_j\Vert }^2}& \mathrm{Eq}.\left(1\right)\end{array}$

[0013] where, μ is a constant called “step gain”, E_jis the output of the error detecting microphone 202, and X_jis a vector expressed by the following Eq.(2) composed of “I” number of elements X_j, X_j−1, . . . X_j(I−1)expressed by X_j(1), X_j(2), . . . , X_j(I) and obtained by the output X_jof the error path filter 230, which simulates the characteristic of the error path leading to the coefficient updating circuit 240 from the output of the multiplier 205 through the error detecting microphone 202, being retraced up to the past I−1 sampling periods.

[0014] X_j=[X_j(1)X_j(1), . . . , X_j(I)]  Eq.(2)

[0015] Also, the noise control filter 220 and the error path filter 230 are composed of a non-recursive type. In the following description, the number of taps in the filters 220 and 230 are expressed by “I” and “M” for the convenience's sake.

[0016] Assuming the Filtered-x NLMS method is a coefficient updating algorithm, the following coefficient of the error path filter 230:

[0017] C=[]  Eq.(3)

[0018] is required to be an estimated value approximated, with a high accuracy, to the following impulse response of the error path:

[0019] C=[C(1)C(2) . . . C(M)]  Eq.(4)

[0020] Generally, the coefficient of the error path filter 230 in FIG. 30 is fixed and the calculation thereof is performed by the arrangement of providing, before starting the active noise control of FIG. 30, a white noise generated by a white noise generation circuit 250, as shown in FIG. 31, to the loud speaker 203 and the error path filter 230, providing the outputs of the error detecting microphone 202 and the error path filter 230 to a subtracter 251, and providing the difference output to the coefficient updating circuit 240.

[0021] Obviously, the problem of such an error path filter is that the white noise is outputted from a white noise generator 130 through the loud speaker to the outside of the duct upon the calculation of the coefficient. In spite of a temporary occurrence, it is not preferable that a noise of another kind is outputted from the active noise control apparatus in that way.

[0022] It is also a problem that the coefficient thus calculated of the error path filter 230 is hereafter to be fixed upon the active noise control as shown in FIG. 30. This is natural because the change of the characteristic within the duct 200 after the calculation can be fully expected.

[0023] In fact, it is known that when the coefficient of the noise control filter 220 is updated by using the calculation result to decrease the noise at the position of the error detecting microphone 202, a reflection position of the noise moves from the outlet end of the duct 200 to the position of the error detecting microphone 202 to change the acoustic characteristic within the duct 200 so that the error path filter 230 fails to accurately simulate the above-mentioned error path.

[0024] This simulating operation with a lowered accuracy may have a bad influence on the accuracy maintenance of the coefficient of the noise control filter 220, whereby a sufficient quantity of the noise reduction can not be obtained, and besides the noise control operation becomes unstable. The fact that the acoustic characteristic within the duct changes along with the decrease of the estimation error of the coefficient of the noise control filter 220 indicates that the coefficient correction of the error path filter 230 is required to be repeatedly performed with the active noise control being kept operated.

[0025] For estimating the coefficient of the error path filter 230 during the active noise control, a method using a circuit arrangement shown in FIG. 32 is known.

[0026] Namely, the white noise generated by the white noise generation circuit 250 is added to the secondary noise −G_jfrom the multiplier 205 at an adder 252 to be outputted from the loud speaker 203, so that the coefficient of the error path filter 230 is updated in order that the output of the subtracter 251 may become a minimum by applying thereto the coefficient updating circuit 240 which is not operating or has become available by not performing (by fixing) the coefficient update of the noise control filter 220, different from the example of FIG. 30.

[0027] In this arrangement, since the coefficient of the error path filter 230 gives the impulse response of the error path whose characteristic has been changed by the noise control at the time when the output of the subtracter 251 has become a minimum, the coefficient at this time has only to be used at the circuit of FIG. 30.

[0028] However, in such a circuit arrangement, as mentioned above, the overlap of the white noise outputted from the loud speaker 203 during the active noise control indicates that the active noise control apparatus becomes a new noise source.

[0029] Furthermore, the Filtered-x NLMS method of the above-mentioned Eq.(1) used for the coefficient update of the error path filter 230 does not guarantee the stable operation of 100%.

[0030] Accordingly, this generally requires a practical compromise to lessen a step gain as much as possible and the possibility of being made unstable. However, since the setting of such a small step gain causes a problem that a noise canceling performance is deteriorated in fixed-point arithmetic, which is practically left unsolved upon adopting an inexpensive fixed-point signal processor.

[0031] In order to fundamentally solve this problem, an algorithm has only to be set up which makes the coefficient calculation of the error path filter 230 unnecessary.

[0032] For such an algorithm, has already been proposed a simultaneous perturbation type optimization technique (Kajikawa, Nomura, “Proposal of Active Noise Control System which Performs Update Only by Using Residual Signal”, 1-4-12, 1997 Autumn Meeting of the Acoustical Society of Japan, pp.497-498).

[0033] The characteristic of this technique lies on the point that perturbation is added to the coefficient of the noise control filter 220 by using the white noise. This measure of adding the perturbation is equivalent to the overlap of the white noise with the secondary noise, which can not solve the problem of the arrangement in FIG. 30.

[0034] Also, the coefficient of the feedback control filter 210 is generally calculated before starting the active noise control by forming the circuit shown in FIG. 33. The calculation method is performed in order that the difference between the output of the feedback path leading to the noise detecting microphone 201 from the loud speaker 203 and the output of the feedback control filter 210 may become a minimum, resulting in that the feedback path is to be intercepted by the subtracter 204.

[0035] However, it is a problem that the coefficient thus calculated of the feedback control filter 210 is hereafter fixed naturally because the change of the characteristic within the duct 200 is fully expected.

[0036] Actually, it is known that when the coefficient of the noise control filter 220 is updated and the noise is canceled at the position of the error detecting microphone 202, the reflect position of the noise moves from the duct outlet to the error detecting microphone 202.

[0037] This change will vary the acoustic characteristic within the duct, so that the characteristic difference between the feedback control filter 210 and the actual feedback path is extended to deteriorate the interception performance of the feedback path.

[0038] This deterioration of the interception performance not only increases the danger of howling occurrence but also increases the estimated coefficient error of the noise control filter 220 and deteriorates the noise reduction performance. The fact that the acoustic characteristic within the duct changes according to the noise reduction quantity means that the coefficient correction of the feedback control filter 210 is required to be repeatedly performed during the active noise control.

[0039] For updating the coefficient of the feedback control filter 210 during the active noise control, a method shown in FIG. 34 is the most general. Namely, the white noise generated by the white noise generation circuit 250 is added to the secondary noise −G_jat the adder 251 to be transmitted from the loud speaker 203, and different from the example of FIG. 30, the coefficient of the feedback control filter 210 is updated in order that the output of the subtracter 204 may become a minimum by applying thereto the coefficient updating circuit 240 which has become available by stopping (fixing) the coefficient update of the noise control filter 220.

[0040] In this arrangement, when the output of the subtracter 204 becomes the minimum, the characteristic of the feedback path which has been changed by the noise control is simulated by the feedback control filter 210, so that the interception of the feedback path is realized.

[0041] However, the defect of this method obviously lies on that a different kind of noise (white noise) from the white noise generation circuit 250 introduced for reducing the noise is transmitted from the loud speaker 203.

[0042] The active noise control apparatus of the feedforward type is shown as an example in the above, while FIG. 35 shows a general arrangement of an active noise control apparatus of a feedback type. This active noise control apparatus reduces a noise w_j[j: sample time index] to be controlled by acoustically overlapping therewith the synthesized noise g_jtransmitted from the loud speaker 203 at the position of the microphone 201. The status of reducing the noise is monitored by the output

[0043] e_j=w_j+g_j  Eq.(5)

[0044] of the microphone 201 and the coefficient updating circuit 240 updates the coefficient of the noise control filter 220 in order that an output e_jmay become the minimum.

[0045] It is to be noted that the error path filter 230 is one for simulating the characteristic of the error path leading to the coefficient updating circuit 240 from the output edge of the noise control filter 220 through a multiplier 221, the loud speaker 203, and the microphone 201, which is required for the coefficient update of the noise control filter 220.

[0046] In addition, when the gain of a closed circuit, formed by the feedback path leading to the microphone 201 from the loud speaker 203 and the noise control filter 220, exceeds “1”, howling occurs. Therefore, in order to prevent the howling, the feedback control filter 210 and an adder (subtracter) 211 are provided.

[0047] As seen from the above Eq.(5), when g_j≈−w_j, the noise w_jis canceled, so that the noise near the microphone 201 becomes small.

[0048] The problem in the active noise control of the feedback type arises from the synthesized noise g_jbeing generated based on the noise w_jto be controlled. Namely, a delay is inevitable until the time when the noise w_jto be controlled is transmitted to the microphone 201 as the synthesized noise g_jafter being received at the microphone 201, synthesized at the noise control filter 220, and inverted at a multiplier 221. Accordingly, the noise which can be controlled with this active noise control apparatus of the feedback type is limited to a periodical noise regardless of the time delay.

[0049] What should be most remarked upon designing this active noise control apparatus is that the apparatus is required to stably operate so as to prevent an opposite effect such as increasing the noise by introducing this apparatus.

[0050] As the most typical adaptive algorithm applied to the coefficient updating circuit 240 which updates the coefficient of the noise control filter 220 in the above-mentioned active noise control apparatus of the feedback type, the above-mentioned Filtered-x method is used in a modified form, in which the error path filter 230 is prepositioned for simulating the characteristic of the path leading to the output of the microphone 201 through the loud speaker 203.

[0051] Namely, if the synthesized noise g_joutputted from the loud speaker 203 shown in FIG. 35 and reaching the microphone 201 is completely canceled by the output of the feedback control filter 210, the input x_jof the noise control filter 220 assumes the noise w_jitself. Accordingly, this input x_jcan be treated as a reference signal for the adaptive algorithm for updating the coefficient of the noise control filter 220.

[0052] Also, the output e_jof the microphone 201 can be regarded as a difference between an output g_jof an adaptive filter, added to a desired response w_jthrough the feedback path leading to the microphone 201 from the loud speaker 203, and the desired response w_j. With these two signals, the arrangement of this feedback type can be treated exactly in the same way as the above-mentioned active noise control apparatus of the feedforward type.

[0053] Namely, a coefficient A_jof the noise control filter 220 in this case is updated by the following equation:

[0054] A_j+1=A_j+μe_jY_j  Eq.(6)

[0055] where Y_j=[Y_j(1)Y_j(2) . . . Y_j(I)]^Tis a signal vector in which “I” number of aggregation of y_j, obtained by applying the error path filter 230 to the input x_jof the noise control filter 220, are replaced by Y_j(i)=y_j−i+1.

[0056] In addition, “I” is the number of taps, and “μ” is a constant called “step gain”.

[0057] A_j=[A_j(1)A_j(2) . . . A_j(I)]^T  Eq.(7)

[0058] is the coefficient of the noise control filter 220 set at the time j.

[0059] In order to stably update the coefficient of the noise control filter 220 by the Filtered-x LMS method, it is required that the impulse response of the feedback path leading to the output of the microphone 201 through the loud speaker 203 is preliminarily calculated and the result is set for the coefficients of the feedback control filter 210 and the error path filter 230.

[0060] The calculation is generally performed by forming the circuit as shown in FIG. 36 with the white noise generation circuit 250 before starting the active noise control. When the output x_jof the subtracter 211 becomes a minimum in this circuit arrangement, it means that the feedback control filter 210 has been able to simulate the feedback path. Then, if the coefficient of the coefficient updating circuit 240 at that time is copied to the error path filter 230, the coefficient update of the noise control filter 220 is made possible by the Filtered-x LMS method.

[0061] The active noise control apparatus of the feedback type applying thereto this coefficient update method is often used, which is mentioned, for example, in the following reference (1):

[0062] (1) Omoto, et al. “The Behavior of an Adaptive Algorithm with Moving Primary Source—Performance of a Feedback System—” 1997 Autumn Meeting of the Acoustical Society of Japan, 1-4-14, pp.501-502).

[0063] The flow of the signals in this active noise control apparatus of the feedback type is equivalently shown by the block diagram of FIG. 37, where

[0064] W(z): transfer function of noise w_j,

[0065] X(z): transfer function of output x_jof subtracter 211,

[0066] E(z): transfer function of output e_jof microphone 201,

[0067] A(z): transfer function of noise control filter 220,

[0068] B(z): transfer function of feedback path leading to output of microphone 201 through loud speaker 203,

[0069] D(z): difference between transfer function B(z) of feedback path and transfer function B(z) of feedback control filter 210.

[0070] In FIG. 37, the coefficient of the noise control filter 220 is updated in order that the output E(z) of the microphone (subtracter) 201 may become a minimum. From FIG. 37, it is seen that the active noise control apparatus of the feedback type can be regarded as a liner predictor for the noise w_jwhich uses the noise control filter 220 as the adaptive filter. As a method proposed by paying attention to this point, an active noise control of an adaptive prediction type exists, which is shown in the following reference (2):

[0071] (2) Hamada, et al. “Active Noise Control Using Adaptive Prediction-Implementation by Adaptive Filter—” 1992 Autumn Meeting of the Acoustical Society of Japan, 2-4-1, pp.531-532.

[0072] The structure controls the filter coefficient of the noise control filter 220 by using an adaptive prediction filter 223 as shown in FIG. 38. Furthermore, the linear prediction analysis portion of this active noise control of the adaptive prediction type would be shown by the block diagram, as shown in FIG. 39, where a(z) is a transfer function of the adaptive prediction filter 223.

[0073] In order to effectively operate the arrangement of this reference (2), in the same way as the reference (1) described before, it is premised that the feedback path is simulated by the feedback control filter 210 with a high accuracy, and the approximation of D(z)≈0 is realized.

[0074] Namely, when $\begin{array}{cc}\frac{1}{1-D\left(z\right)A\left(z\right)}\approx 1& \mathrm{Eq}.\left(8\right)\end{array}$

[0075] is realized, the output X(z) of the subtracter 211 assumes the noise W(z) itself.

[0076] Furthermore, since the approximation is also B(z)={circumflex over (B)}(z), it is seen that the arrangements of FIGS. 39 and 37 form a linear prediction analysis circuit for the noise W(z) having the same structure, if these two approximations of D(z)=0 and B(z)={circumflex over (B)}(z) are applied to the circuit arrangement of FIG. 37 to exchange the connection order of the transfer function A(z) of the noise control filter 220 and the transfer function B(z) of the feedback path.

[0077] Namely, as the result of the linear prediction analysis by the circuit arrangement of FIG. 39, when the output of a subtracter 222 becomes a minimum, the coefficient of the adaptive prediction filter 223 provides the coefficient of the noise control filter 220 which minimizes the output E(z) of the microphone 201. Accordingly, when the coefficient of the adaptive prediction filter 223 is copied for the coefficient of the noise control filter 220, the noise w_jis suppressed small.

[0078] However, the problem in this case is that the control principles of the active noise control apparatuses of the feedback type in FIGS. 35 and 38 both premise B(z)={circumflex over (B)}(z).

[0079] Generally, in the estimate of the impulse response of the feedback path the error is inevitable, so that it is fully expected that the response changes with time. However, it is possible to take a measure that the coefficient of the feedback control filter 210 is updated all the time to maintain B(z)={circumflex over (B)}(z) by overlapping the white noise with the synthesized noise to make it a reference signal. However, feeding the white noise to the secondary source is equal to making the active noise control apparatus a new noise source.

[0080] In the active noise control apparatus of FIG. 35, as another defect, “coefficient updating algorithm of Filtered-x type represented by Filtered-x LMS method is unstable in principle” can be mentioned.

[0081] The stability condition of the Filtered-x LMS method is studied in the following reference (3):

[0082] (3) Yabuki, et al. “Stability Condition in Filtered-x LMS Method in case that Modeled Error Exists in C Filter” The institute of electronics, information and communication engineers, (A), vol J80-A no.11, pp.1868-1876 (1997-11).

[0083] However, as a result, measures except “providing smallest step gain” are not mentioned. Also, according to the analysis, even if the step gain is made small, the stability can not be completely guaranteed.

[0084] It is accordingly an object of the present invention to provide an active noise control apparatus for updating a coefficient of a noise control filter which synthesizes a secondary noise having a same amplitude as and an opposite phase to a noise to be suppressed, in which an algorithm not requiring a coefficient calculation of an error path filter without outputting a white noise from a loud speaker is set up, thereby fundamentally solving the problem of Filtered-x LMS method.

[0085] Furthermore, it is an object of the present invention to provide an active noise control apparatus which has a function of correcting a coefficient of a feedback control filter all the time corresponding to a changing impulse response of a feedback path without outputting the white noise from the loud speaker during the noise control.

[0086] Moreover, it is an object of the present invention to provide an active noise control apparatus of a feedback type having a feedback control filter which simulates a characteristic of a feedback path leading to a noise detecting microphone connected to an input of a noise control filter for synthesizing a secondary noise, through a loud speaker which transmits the secondary noise having the same amplitude as and the opposite phase to a primary noise for suppression, and which realizes an updating circuit of an essentially stable coefficient for the noise control filter without outputting the white noise from the loud speaker.

[0087] FIG. 1 shows a principle of an active noise control apparatus according to the present invention [1], and in particular is a diagram for illustrating a calculation principle of a coefficient of a noise control filter not requiring a coefficient estimation of an error path filter used for the active noise control apparatus.

[0088] In the present invention, the noise control filter comprises a first and a second noise control filter 144 and 142 respectively having a first and a second arbitrary coefficient A₁and A₂, and the apparatus further comprises a first and a second overall system filter 141 and 143 which form an overall system filter for simulating a characteristic of an overall system leading to an error detecting microphone from a noise detecting microphone that detects a noise component required for synthesizing the secondary noise, and which has a first and a second coefficient S₁and S₂respectively obtained for the second and the first coefficient A₁and A₂, a differential overall system filter 146 for outputting a response difference of the first and the second overall system filter 141 and 143, and an estimating noise transfer system filter 147, having a variable coefficient, connected to the differential overall system filter 146 in cascade, a white noise generated by a white noise generation circuit 250 being applied to the differential overall system filter 146 and to respective cascade combinations of the first overall system filter 141 and the second noise control filter 142, and the second overall system filter 143 and the first noise control filter 144; the coefficient of the estimating noise transfer system filter 147 being updated in order that a difference between the output of the differential overall system filter 146 and a differential output between the first and the second noise control filter 144 and 142 becomes a minimum, and the coefficient of the estimating noise transfer system filter 147 obtained at a time when the difference becomes the minimum being provided as the coefficients of the noise control filters.

[0089] In order to briefly explain the principle, the active noise control apparatus of FIG. 30 is shown by a functional block diagram as shown in FIG. 2. However, since the subtraction of the noise by the secondary noise is performed within a space of the duct 200 in FIG. 2, a subtracter 206 shown in FIG. 2 is not formed as an actual circuit. Also, being not related to the principle, the feedback control filter 210 is omitted in FIG. 2.

[0090] Also, the basic arrangement of the active noise control apparatus when the arrangement of FIG. 2 is applied to the present invention is shown in FIG. 3, wherein it is characterized that an overall system filter 260 for simulating the overall characteristic of the control system leading to the error detecting microphone 202 from the noise detecting microphone 201 is added.

[0091] Since the coefficient of the noise control filter 220 is arbitrarily set, the first and the second noise control filter 144 and 142 forming the noise control filter 220 shown in FIG. 3 are set to have a first and a second coefficient A₁and A₂so that the transfer functions are made to have the coefficients A₁and A₂by modifying the coefficient to the extent of the noise reduction quantity being not deteriorated greatly.

[0092] In addition, the first and the second coefficient S₁and S₂of the overall system filter 260, which makes an output of a subtracter 261 a minimum for the first and the second coefficient A₁and A₂set in the noise control filter 220 in the arrangement of FIG. 3, are set in the first and second overall system filter 141 and 143 shown in FIG. 1.

[0093] The differential overall system filter 146 is one for generating a difference output S₁−S₂between the first and the second overall system filter 141 and 143. The estimating noise transfer system filter 147 is an adaptive filter for updating the coefficient in order that the output of a subtracter 148 may become a minimum by the coefficient updating circuit 240 applied from the active noise control apparatus of FIG. 3 by using a signal obtained by applying the output of the white noise generation circuit 250 to the first and the second overall system filter 141 and 143 and the differential overall system filter 146, thereby extracting the impulse response of the noise transfer system as a coefficient, included in the first and the second overall system filter 141 and 143, and the first and the second noise control filter 142 and 144.

[0094] The calculation of the coefficient of the overall system filter 260 shown in FIG. 3 is performed by temporarily stopping the coefficient update of the noise control filter 220 and applying thereto the coefficient updating circuit 240 which has become unnecessary by the stoppage. Expressing the transfer functions of the circuit shown in FIG. 3 respectively as follows:

[0095] D: transfer function of noise transfer system 200,

[0096] A: transfer function of noise control filter 220,

[0097] S: transfer function of overall system filter 260,

[0098] C: transfer function of error path 190,

[0099] the relationship of the following equation is obtained when the output of the subtracter 261 becomes the minimum:

[0100] S≈(D−A)C  Eq.(9)

[0101] It is of course that since the coefficients of the noise control filter 220 can be arbitrarily set, the coefficients are set in order that the transfer functions may assume A₁and A₂by modifying the coefficients to the extent of the noise reduction quantity being deteriorated greatly, and the coefficients of the overall system filter 260 are updated in order that the output of the subtracter 261 may become the minimum for both coefficients.

[0102] When the output of the subtracter 261 has become the minimum by the coefficient update, the transfer functions S₁and S₂of the overall system filter 260 satisfy the following equations:

[0103] S₁≈(D−A₁)C  Eq.(10)

[0104] S₂≈(D−A₂)C  Eq.(11)

[0105] Obviously, with the difference between the above-mentioned both transfer functions S₁and S₂, the transfer function D of the noise transfer system 200 is eliminated, so that the transfer function of the error path to be determined, i.e. the coefficient of the error path filter 230 is calculated by the following equation:

[0106] C≈(S₁−S₂)/(A₂−A₁)  Eq.(12)

[0107] From the first and the second Eqs.(10) and (11) of the simultaneous equations, it is seen that the transfer function D of the noise transfer system 200 is included as another unknown number. If “D” is solved with Eqs.(10) and (11), the following equation can be obtained:

[0108] D=(S₁A₂−S₂A₁)/(S₁−S₂)  Eq.(13)

[0109] Then, the transfer function of the left side of Eq.(13) has only to be converted into the impulse response. The sampled values of the impulse response assume the coefficient of the noise control filter 220 to be determined.

[0110] Namely, by taking advantage of a coefficient of a non-recursive filter corresponding to the impulse response, the characteristics of the systems are modified by the impulse response from the transfer function. Firstly, the impulse response in the noise transfer system 200 is expressed as in the following equation:

[0111] D=[D(1)D(2) . . . D(I)]  Eq.(14)

[0112] The coefficients corresponding to the transfer functions S₁and S₂of the overall system filter 260 are respectively expressed as follows:

[0113] S₁=[S₁(1)S₁(2) . . . S₁(L)]  Eq.(15)

[0114] S₂=[S₂(1)S₁(2) . . . S₂(L)]  Eq.(16)

[0115] Also, two coefficients of the noise control filter 220 are expressed as follows:

[0116] A₁=[A₁(1)A₁(2) . . . A₁(I)]  Eq.(17)

[0117] A₂=[A₂(1)A₂(2) . . . A₂(I)]  Eq.(18)

[0118] If S₁is provided to the first overall system filter 141 of the circuit shown in FIG. 1, S₂to the second overall system filter 143, and similarly the coefficients A₁and A₂are respectively provided to the first and the second noise control filter 144 and 142 by using the above-mentioned equations, the output of a subtracter 145 assumes a response whose transfer function is S₁A₂−S₂A₁.

[0119] Accordingly, if the estimating noise transfer system filter 147 having a variable coefficient is connected to the differential overall system filter 146 in cascade whose filter coefficient is S₁−S₂with the system whose transfer function S₁A₂−S₂A₁being made an unknown system, and the coefficient of the estimating noise transfer system 147 is updated at the coefficient updating circuit 240 in order that the output of the subtracter 148 may become the minimum, the coefficient converges into the impulse response of the noise transfer system 200.

[0120] It is to be noted that only upon the activation preliminarily stored coefficients may be used for the first and the second coefficient respectively of the above-mentioned first and the second noise control filter, and after the activation a coefficient obtained upon the present coefficient update may be substituted for one of the first and the second coefficient, and furthermore, coefficients obtained upon the last and the present coefficient update may be provided for the first and the second coefficient.

[0121] Also, when the output of the overall system filter becomes equal to or less than a threshold value, it is preferable that the coefficient update is stopped.

[0122] FIG. 4 is a principle diagram of an active noise control apparatus according to the present invention [2]. An inverse filter composing circuit 110 forms a filter having a characteristic including a transfer function opposite to a closed circuit starting from the noise control filter 220 and returning to the noise control filter 220 again through both (parallel circuit) of the feedback path and the feedback control filter 210, the transfer function expressing a generation process of the primary noise.

[0123] A system identification circuit 120 provides two pairs of different fixed coefficients either to the feedback control filter 210 or the noise control filter 220 to update a coefficient of an adaptive filter 150 in order that a difference becomes a minimum between an output of a first filter 130 forming a numerator of a solution obtained by eliminating a transfer function component expressing the generation process of the primary noise, from simultaneous equations based on two transfer functions of an inverse filter formed within the inverse filter composing circuit 110 for the two pairs of coefficients and an output of the adaptive filter 150 connected to a second filter 140 in cascade forming a denominator of the solution.

[0124] A coefficient of the feedback control filter 210 is updated by using the coefficient of the adaptive filter 150 obtained by operating the system identification circuit 120.

[0125] The principle of the present invention is an improvement of an active noise control apparatus of the Japanese Patent Application No.9-239776 (Japanese Patent Publication Laid-open No.11-85165) by the inventors of this invention and others.

[0126] The principle will be briefly described referring to FIG. 5.

[0127] Firstly, in the system where the active noise control can be applied, the primary noise is not supposed to be a white noise. If the application to a practical apparatus is considered, this supposition is natural.

[0128] At this time, the noise x_jwhich is detected at the noise detecting microphone 201 and which is not the white noise can be regarded as the output of the filter W(z) (represented by “W” in Figure, and hereinafter will be represented similarly) which inputs a white noise W_j.

[0129] The feature of this apparatus lies in that before starting the active noise control, a filter W⁻¹(z) having an inverse characteristic to a noise generation filter W(z) is preliminarily formed by a whitening circuit 310 shown in the upper part of FIG. 5.

[0130] This whitening circuit 310 can be formed by using, for example, a linear prediction method common in a voice analysis field. It can be said that the whitening circuit 310 has formed the inverse filter W⁻¹(z) when the noise x_jis whitened.

[0131] On the other hand, the output from the subtracter 204 after starting the active noise control becomes w_j·W(z)/{1−D(z)A(z)}, where D(z) is a difference between a transfer function {circumflex over (B)}(z) of the feedback control filter 210 and a transfer function B(z) of the feedback path (feedback path within the duct 200 from the loud speaker 203 to the microphone 201), and A(z) is a transfer function of the noise control filter 220.

[0132] Accordingly, the signal outputted as a result that the inverse filter W⁻¹(z) by the whitening circuit 310 is operated on the output of the subtracter 204 assumes an output in which a white noise w_jis applied to the system whose transfer function is W(z)W⁻¹(z)/{1−D(z)A(z)}, so that it is expressed by w_j·W(z)W⁻¹(z)/{1−D(z)A(z)}.

[0133] Obviously, since the numerator W(z)W⁻¹(z) represents a simple delay, the coefficient of the inverse filter formed by the inverse filter composing circuit 110 assumes {1−D(z)A(z)}, if the above-mentioned output of the whitening circuit 310 is similarly whitened by using the composing circuit 110.

[0134] Furthermore, if an inverse filter 320 which provides the transfer function as {1−D(z)A(z)} is combined with a subtracter 330, the transfer function is given by the following equation:

[0135] 1−{1−D(z)A(z)}=D(z)A(z)  Eq.(19)

[0136] Accordingly, if this transfer function is made an unknown system function and the system identification circuit is formed by connecting the cascade connection of a copied noise control filter 360 formed by copying the coefficient of the noise control filter 220 and the adaptive filter 150 to the unknown system in parallel, the adaptive filter 150 at the time when the output of a subtracter 151 becomes the minimum is to provide a transfer function approximated to the above-mentioned transfer function D(z), since the transfer function of the copied noise control filter 360 is A(z) as mentioned above.

[0137] Namely, if the coefficient of the adaptive filter 150 is added to that of the feedback control filter 210 to be updated, the gain of a closed circuit formed by the feedback path is to be suppressed small.

[0138] However, in the apparatus mentioned in the Japanese Patent Application No.9-239776 (Japanese Patent Publication Laid-open No.11-85165) as mentioned above, that “it is necessary that the inverse filter W⁻¹(z) of the filter W(z) which generates the noise x_jis formed before starting the active noise control” makes an issue.

[0139] Obviously, if the characteristic of the noise x_jcan change during the active noise control, the inverse filter composing circuit 110 does not compose the transfer function {1−D(z)A(z)}, and can not be applied to the system where the characteristic of the noise changes during the active noise control.

[0140] Therefore, in the present invention [2], the noise x_jdetected at the noise detecting microphone 201 is assumed to be the output of the filter W(z) for the white noise w_j, in the same way as the present invention [1], while the process of estimating the inverse filter W⁻¹(z) before starting the active noise control is not performed. Accordingly, the whitening circuit 310 in FIG. 5 is removed from the schematic diagram of the present invention in FIG. 4.

[0141] In the present invention, the same supposition as the linear prediction analysis of the voice, i.e. the process of generating the noise x_jis supposed to be described by an all-pole model 1/{1−P(z)}. At this time, the output x(z) of the subtracter 204 obtained during the active noise control is as follows: $\begin{array}{cc}X\left(z\right)=\frac{1}{\left\{1-P\left(z\right)\right\}\left\{1-D\left(z\right)A\left(z\right)\right\}}=\frac{1}{1-P\left(z\right)-D\left(z\right)A\left(z\right)+P\left(z\right)D\left(z\right)A\left(z\right)}& \mathrm{Eq}.\left(20\right)\end{array}$

[0142] If this output is provided to the input of the inverse filter composing circuit 110 in FIG. 4 and the inverse filter X⁻¹(z) is formed within the inverse filter composing circuit 110 by applying thereto e.g. the linear prediction analysis method, the coefficient of the inverse filter whose transfer function is

[0143] X⁻¹(z)=1−P(z)−D(z)A(z)+P(z)D(z)A(z)  Eq.(21)

[0144] can be obtained.

[0145] In this inverse filter X⁻¹(z), two unknown transfer functions P(z) and D(z) are included. In order to eliminate one of the unknown number P(z) and extract the other unknown number D(z) which is the object of the present invention, two independent equations (simultaneous equations) are required.

[0146] In the present invention, as a method for obtaining the two independent equations, a method is adopted for forming two transfer functions X₁⁻¹(z) and X₂⁻¹(z), which can be realized by providing two pairs of independent coefficients to the noise control filter 220 or the feedback control filter 210 (see FIG. 30) at the inverse filter composing circuit 110.

[0147] (2-1) Case of Providing Two Pairs of Fixed Coefficients to Noise Control Filter 220:

[0148] This case takes advantage of the coefficients of the noise control filter 220 being arbitrarily set if the decrease of the noise reduction quantity is allowed. Namely, if the coefficients of noise control filter 220 is modified with a time interval to the extent that the noise reduction quantity does not excessively lower below an allowable range so that two pairs of coefficients forming two different transfer functions A₁(z) and A₂(z) of the noise control filter 220 are provided, the inverse filter composing circuit 110 composes the inverse filters whose transfer functions are respectively given by the following equations for each pair of the coefficients:

[0149] X₁⁻¹(z)=1−P(z)−D(z)A₁(z)+P(z)D(z)A₁(z)  Eq.(22)

[0150] X₂⁻¹(z)=1−P(z)−D(z)A₂(z)+P(z)D(z)A₂(z)  Eq.(23)

[0151] In this case, the transfer functions X₁⁻¹(z) and X₂⁻¹(z) are obtained, if the transfer functions A₁(z) and A₂(z) are respectively determined.

[0152] If the both equations are transformed as $\begin{array}{cc}P\left(z\right)=\frac{1-X_1^{-1}\left(z\right)-D\left(z\right)A_1\left(z\right)}{1-D\left(z\right)A_1\left(z\right)}& \mathrm{Eq}.\left(24\right)\\ P\left(z\right)=\frac{1-X_2^{-1}\left(z\right)-D\left(z\right)A_2\left(z\right)}{1-D\left(z\right)A_2\left(z\right)}& \mathrm{Eq}.\left(25\right)\end{array}$

[0153] and the unknown number P(z) is eliminated, and the equation is arranged for the other unknown number D(z), the following equation can be obtained: $\begin{array}{cc}D\left(z\right)=\frac{X_2^{-1}\left(z\right)-X_1^{-1}\left(z\right)}{A_1\left(z\right)X_2^{-1}\left(z\right)-A_2\left(z\right)X_1^{-1}\left(z\right)}& \mathrm{Eq}.\left(26\right)\end{array}$

[0154] The right side of Eq.(26) is all composed of known transfer functions, and the left side D(z) is, as mentioned above, the difference between the transfer function {circumflex over (B)}(z) of the feedback control filter 210 and the transfer function B(z) of the feedback path. Therefore, if the filter coefficient composing the transfer function of Eq.(26) is added to the coefficient of the feedback control filter 210, the transfer function B(z) of the feedback path can be obtained, whereby the object of the present invention can be achieved.

[0155] (2-2) Case of Providing Two Pairs of Fixed Coefficients to Feedback Control Filter 210:

[0156] The coefficients of the feedback control filter 210 can also be set arbitrarily, if the increase of the feedback quantity is allowed. Namely, the coefficients of the feedback control filter 210 is modified to the extent that the howling does not occur as follows:

[0157] D₁(z)=B(z)−{circumflex over (B)}₁(z)  Eq.(27)

[0158] D₂(z)=B(z)−{circumflex over (B)}₂(z)  Eq.(28)

[0159] By these equations, the inverse filter composing circuit 110 composes the inverse filters whose transfer functions are as follows:

[0160] X₁⁻¹(z)=1−P(z)−{B(z)−{circumflex over (B)}₁(z)}A(z)+P(z){B(z)−{circumflex over (B)}₁(z)}A(z)  Eq.(29)

[0161] X₂⁻¹(z)=1−P(z)−{B(z)−{circumflex over (B)}₂(z)}A(z)+P(z){B(z)−{circumflex over (B)}₂(z)}A(z)  Eq.(30)

[0162] If both equations are arranged to eliminate the unknown number P(z) as follows: $\begin{array}{cc}P\left(z\right)=\frac{1-X_1^{-1}\left(z\right)-\left\{B\left(z\right)-{\hat{B}}_1\left(z\right)\right\}A\left(z\right)}{1-\left\{B\left(z\right)-{\hat{B}}_1\left(z\right)\right\}A\left(z\right)}& \mathrm{Eq}.\left(31\right)\\ P\left(z\right)=\frac{1-X_2^{-1}\left(z\right)-\left\{B\left(z\right)-{\hat{B}}_2\left(z\right)\right\}A\left(z\right)}{1-\left\{B\left(z\right)-{\hat{B}}_2\left(z\right)\right\}A\left(z\right)}& \mathrm{Eq}.\left(32\right)\end{array}$

[0163] and both are assumed equal, the following equation can be obtained:

[0164] [1−X₂⁻¹(z)−{B(z)−{circumflex over (B)}₂(z)}A(z)−][1−{B(z)−{circumflex over (B)}₁(z)}A(z)]=

[0165] [1−X₁⁻¹(z)−{B(z)−{circumflex over (B)}₁(z)}A(z)−][1−{B(z)−{circumflex over (B)}₂(z)}A(z)]  Eq.(33)

[0166] If this equation is arranged for the other unknown number B(z), the following equation can be obtained: $\begin{array}{cc}B\left(z\right)=\frac{X_2^{-1}\left(z\right)-X_1^{-1}\left(z\right)+A\left(z\right)\left\{{\hat{B}}_1\left(z\right)X_2^{-1}\left(z\right)-{\hat{B}}_2\left(z\right)X_1^{-1}\left(z\right)\right\}}{A\left(z\right)\left\{X_2^{-1}\left(z\right)-X_1^{-1}\left(z\right)\right\}}& \mathrm{Eq}.\left(34\right)\end{array}$

[0167] This B(z) is a transfer function of the feedback path as mentioned above, and all of the transfer functions on the right side are known. Accordingly, if the filter coefficient forming the transfer function B(z) is reset to the feedback control filter 210, the response of the feedback path in the duct 200 is canceled, so that the gain of the closed circuit is decreased.

[0168] (2-3) Calculation of Coefficient by System Identification Circuit 120:

[0169] The circuit for calculating the filter coefficient forming Eq.(26) or Eq.(34) is hereby required. In the present invention, the calculation is performed by using the technique of the system identification.

[0170] Firstly, if the adaptive filter 150 whose transfer function is supposed to be d(z) is introduced to update the coefficient of the adaptive filter 150 in order that the difference between the output of the first filter 130 having the numerator of Eq.(26) as the transfer function, as shown in FIG. 4, and the output of the cascade connection of the second filter 140 and the adaptive filter 150 having the denominator of Eq.(26) as the transfer function may become the minimum, the cascade connection of the filters 140 and 150 are approximated to the same numerator (filter 130) upon the convergence of the coefficient of the adaptive filter 150, so that the numerator is equal to [A₁(z)X₂⁻¹(z)−A₂(z)X₁⁻¹(z)]D(z) for Eq.(26).

[0171] Namely, after the convergence, the coefficient of the adaptive filter 150 is to provide the transfer function d(z) approximated to D(z).

[0172] Accordingly, if the adaptive filter 150 and the feedback control filter 210 are similarly formed, by adding the coefficient of the adaptive filter 150 to that of the feedback control filter 210 the coefficient can be replaced by the coefficient which decreases the gain of the closed circuit.

[0173] This procedure is similarly applied to the method (by Eq.(34)) of performing the update by providing two pairs of fixed coefficients to the feedback control filter 210. The coefficients forming the transfer functions of the numerator and the denominator of Eq.(34) have only to be set in the first and the second filter 130 and 140 in FIG. 4.

[0174] It is to be noted that the above-mentioned system identification circuit can be transformed as follows:

[0175] To form the simultaneous equations by using a transfer function provided by the inverse filter composing circuit, from which a constant 1 is removed.

[0176] To form the simultaneous equations by setting the two pairs of fixed coefficients of the noise control filter or the feedback control filter to different taps upon the activation of the apparatus.

[0177] To set the two pairs of fixed coefficients of the noise control filter or the feedback control filter with a time interval.

[0178] To use coefficients obtained upon the last activation for the two pairs of fixed coefficients of the noise control filter or the feedback control filter upon the activation of the apparatus.

[0179] Not to update the coefficient of the feedback control filter when the gain of the adaptive filter becomes equal to or less than a fixed value upon a coefficient update performed by providing the two pairs of fixed coefficients to the noise control filter.

[0180] FIG. 6 shows a principle arrangement of an active noise control apparatus of a feedback type according to the present invention [3]. An inverse filter composing circuit 110 is one which forms a filter having a characteristic including a transfer function opposite to a closed circuit starting from the noise control filter 220 and returning to the noise control filter 220 again through both (parallel circuit) of the feedback path and the feedback control filter 210, the transfer function expressing a generation process of the primary noise.

[0181] A system identification circuit 120 is one for providing two pairs of different fixed coefficients either to the feedback control filter 210 or the noise control filter 220 and for identifying the transfer function of the feedback path by updating a coefficient of an adaptive filter 123 in order that a difference becomes a minimum between an output of a first filter 121 forming a numerator of a solution obtained by eliminating the transfer function component expressing the generation process of the primary noise, from simultaneous equations based on two transfer functions of an inverse filter formed within the inverse filter composing circuit 110 for the two pairs of coefficients and an output of the adaptive filter 123 connected to a second filter 122 in cascade forming a denominator of the solution.

[0182] Also, the system identification circuit 120 is repeatedly used for calculating the coefficient of the noise control filter 220 optimally canceling the primary noise, makes a numerator of a ratio of the transfer function expressing the generation process of the primary noise obtained from the simultaneous equations and the transfer function of the feedback path, the first filter 121, makes a denominator the second filter 122, so that the coefficient of the noise control filter 220 which optimally cancels the primary noise is calculated for that of the adaptive filter 123 which minimizes the output of the subtracter 124.

[0183] The operation principle of the active noise control apparatus of the feedback type shown in FIG. 6 will now be described.

[0184] The noise canceled by the active noise control apparatus of the feedback type is limited to a correlation component of the noise w_j. The generation process of the correlation component of the noise w_jcan be expressed as the all-pole model, and the noise W(z) can be expressed as the following equation with the white Gaussian noise being inputted: $\begin{array}{cc}W\left(z\right)=\frac{1}{1-P\left(z\right)}& \mathrm{Eq}.\left(35\right)\end{array}$

[0185] When the synthesized noise g_jsuccessfully cancels the correlation component of this noise w_j, and the output e_jof the microphone 201 is whitened, the output E(z) of the microphone in FIG. 37 becomes “1” in the following equation: $\begin{array}{cc}\begin{array}{c}E\left(z\right)=W\left(z\right)\left\{1-\frac{A\left(z\right)B\left(z\right)}{1-D\left(z\right)A\left(z\right)}\right\}\\ =\frac{1}{1-P\left(z\right)}\left\{1-\frac{A\left(z\right)B\left(z\right)}{1-D\left(z\right)A\left(z\right)}\right\}\end{array}& \mathrm{Eq}.\left(36\right)\end{array}$

[0186] If Eq.(36) is arranged by applying E(z)=1, the following equation can be obtained: $\begin{array}{cc}P\left(z\right)=\frac{A\left(z\right)B\left(z\right)}{1-D\left(z\right)A\left(z\right)}& \mathrm{Eq}.\left(37\right)\end{array}$

[0187] If Eq.(37) is arranged for the transfer function A(z) of the noise control filter 220, the following equation is obtained: $\begin{array}{cc}A\left(z\right)=\frac{P\left(z\right)}{B\left(z\right)+P\left(z\right)D\left(z\right)}& \mathrm{Eq}.\left(38\right)\end{array}$

[0188] Therefore, it is seen that the noise becomes the minimum when the coefficient forming the transfer function A(z) is provided to the noise control filter 220.

[0189] It is to be noted that

[0190] D(z)=B(z)−{circumflex over (B)}(z)  Eq.(39)

[0191] Namely, in order to obtain the transfer function A(z), the transfer functions B(z) and P(z) have only to be obtained.

[0192] The signals which can be monitored by the active noise control apparatus of the feedback type are only the output e_jof the microphone 201 and the output x_jof the subtracter 211. According to the arrangement of FIG. 37, the output x_jof the subtracter 211 can be obtained as $\begin{array}{cc}\begin{array}{c}X\left(z\right)=\frac{W\left(z\right)}{1-D\left(z\right)\hat{A}\left(z\right)}\\ =\frac{1}{1-P\left(z\right)-D\left(z\right)\hat{A}\left(z\right)+P\left(z\right)D\left(z\right)\hat{A}\left(z\right)}\end{array}& \mathrm{Eq}.\left(40\right)\end{array}$

[0193] by substituting the above Eq.(35) when the coefficient whose transfer function is Â(z) is set in the noise control filter 220.

[0194] In the present invention, the inverse filter X⁻¹(z) can be obtained for the output X(z) by using the inverse filter composing circuit 110. For instance, when the inverse filter composing circuit 110 is applied to the output X(z) shown in FIG. 7, the coefficient whose transfer function is

[0195] S(z)=P(z)+D(z)Â(z)−P(z)D(z)Â(z)  Eq.(41)

[0196] is set in a non-recursive filter 271 when the output of a subtracter 272 becomes the minimum.

[0197] In this transfer function S(z), the unknown numbers P(z) and D(z) (i.e. B(z)) forming Eq.(38) are included. In order to calculate two unknown numbers P(z) and D(z), the equation obtained as Eq.(41) is not enough, so that another equation is required.

[0198] As a method for obtaining the two equations, as shown in the present invention [2], the fact that an arbitrary fixed coefficient can be set in the noise control filter 220 or the feedback control filter 210 can be utilized.

[0199] Namely, when two pairs of independent fixed coefficients are provided to the noise control filter 220 or the feedback control filter 210, the inverse filter composing circuit 110 provides two transfer functions S₁(z) and S₂(z) to the two pairs of coefficients, with which two equations (simultaneous equations) can be obtained as follows:

[0200] (3-1) Case of Providing Two Pairs of Coefficients to Noise Control Filter 220:

[0201] It is assumed that a slight decline of the noise reduction quantity can be allowed. Namely, if the coefficient A(z) of the noise control filter 220 is modified to the extent of the noise reduction quantity being not deteriorated greatly, and two pairs of coefficients forming two different transfer functions A₁(z) and A₂(z) are provided, the inverse filter composing circuit 110 composes the non-recursive filter 271 whose transfer functions as follows for the two coefficients:

[0202] S₁(z)=P(z)+D(z)A₁(z)−P(z)D(z)A₁(z)  Eq.(42)

[0203] S₂(z)=P(z)+D(z)A₂(z)−P(z)D(z)A₂(z)  Eq.(43)

[0204] If both equations are transformed as $\begin{array}{cc}P\left(z\right)=\frac{S_1\left(z\right)-D\left(z\right)A_1\left(z\right)}{1-D\left(z\right)A_1\left(z\right)}& \mathrm{Eq}.\left(44\right)\\ P\left(z\right)=\frac{S_2\left(z\right)-D\left(z\right)A_2\left(z\right)}{1-D\left(z\right)A_2\left(z\right)}& \mathrm{Eq}.\left(45\right)\end{array}$

[0205] and one unknown number P(z) is eliminated, one of the two unknown numbers can be obtained as follows: $\begin{array}{cc}D\left(z\right)=\frac{S_1\left(z\right)-S_2\left(z\right)}{A_1\left(z\right)\left\{1-S_2\left(z\right)\right\}-A_2\left(z\right)\left\{1-S_1\left(z\right)\right\}}& \mathrm{Eq}.\left(46\right)\end{array}$

[0206] It is to be noted that the transfer functions S₁(z) and S₂(z) can be obtained if the transfer functions A₁(z) and A₂(z) are determined by using the non-recursive filter 271 of FIG. 7.

[0207] Accordingly, the right side of Eq.(46) is all composed of known transfer functions, so that it is seen that the difference D(z) between the transfer function B(z) of the feedback control filter 210 and the transfer function B(z) of the feedback path can be calculated.

[0208] As shown in FIG. 6, if the numerator of Eq.(46) is obtained by the first filter 121, the denominator of Eq.(46) is obtained by the second filter 122, and the coefficient of the adaptive filter 123 is updated in order that no difference from the subtracter 124 is found, the transfer function D(z) can be obtained.

[0209] Similarly, from Eqs.(42) and (43), the left unknown number P(z) can be solved. Namely, the unknown transfer function D(z) is arranged as $\begin{array}{cc}D\left(z\right)=\frac{S_1\left(z\right)-P\left(z\right)}{A_1\left(z\right)\left\{1-P\left(z\right)\right\}}& \mathrm{Eq}.\left(47\right)\\ D\left(z\right)=\frac{S_2\left(z\right)-P\left(z\right)}{A_2\left(z\right)\left\{1-P\left(z\right)\right\}}& \mathrm{Eq}.\left(48\right)\end{array}$

[0210] and then both is assumed equal, so that the following equation can be obtained: $\begin{array}{cc}P\left(z\right)=\frac{S_2\left(z\right)A_1\left(z\right)-S_1\left(z\right)A_2\left(z\right)}{A_1\left(z\right)-A_2\left(z\right)}& \mathrm{Eq}.\left(49\right)\end{array}$

[0211] Namely, the determined transfer function A(z) of the noise control filter 220 which optimally cancels the noise x_jto be controlled can be obtained by substituting D(z) and P(z), which are obtained by calculating the above-mentioned Eqs.(46) and (49), as well as the present transfer function {circumflex over (B)}(z) of the feedback control filter 210 for the following equation: $\begin{array}{cc}A\left(z\right)=\frac{P\left(z\right)}{\hat{B}\left(z\right)+\left\{1+P\left(z\right)\right\}D\left(z\right)}& \mathrm{Eq}.\left(50\right)\end{array}$

[0212] in which Eq.(39) is substituted for Eq.(38) to be arranged.

[0213] However, the transfer function of the feedback path (loud speaker 203→microphone 201) has improved its accuracy more than the present transfer function at this point is obtained as follows from Eq.(46):

[0214] {tilde over (B)}(z)={circumflex over (B)}(z)+D(z)=B(z)  Eq.(51)

[0215] Otherwise, a correction of making {tilde over (B)}(z) a new transfer function of the feedback path would be more natural.

[0216] Therefore, the transfer function of the feedback path is changed into {tilde over (B)}(z) of Eq.(51). At this time, since the transfer function A(z) of the noise control filter 220 which optimally cancels the noise x_jto be controlled is approximated to D(z)=0 for the new transfer function {tilde over (B)}(z) of the feedback path, the transfer function A(z) can be calculated from the following equation by Eqs.(50) and (51): $\begin{array}{cc}A\left(z\right)=\frac{P\left(z\right)}{\tilde{B}\left(z\right)}& \mathrm{Eq}.\left(52\right)\end{array}$

[0217] By obtaining the numerator P(z) in Eq.(52) at the first filter 121 in FIG. 6 and the denominator {tilde over (B)}(z) at the second filter 122, the coefficient a(z) of the adaptive filter 123 is updated in order that the output of the subtracter 124 may become “0”, so that the transfer function A(z) can be obtained.

[0218] (3-2) Case of Providing Two Pairs of Coefficients to Feedback Control Filter 210:

[0219] In the same way as the case of the noise control filter 220, the coefficients of the noise control filter 210 can be arbitrarily set if the increase of the feedback quantity is temporarily allowed. Namely, the coefficients whose transfer function assumes Â(z) are provided to the noise control filter 220, and the coefficients is modified to the extent that the howling does not occur to the feedback control filter 210, so that the coefficients are set in order that the difference D(z) may become as follows:

[0220] D₁(z)=B(z)−{circumflex over (B)}₁(z)  Eq.(53)

[0221] D₂(z)=B(z)−{circumflex over (B)}₂(z)  Eq.(54)

[0222] By these equations, the inverse filter composing circuit 110 composes the non-recursive filter 271 whose transfer functions are respectively as follows:

[0223] S₁(z)P(z)+{B(z)−{circumflex over (B)}₁(z)}Â(z)−P(z){B(z)−{circumflex over (B)}₁(z)}Â(z)  Eq.(55)

[0224] S₂(z)P(z)+{B(z)−{circumflex over (B)}₂(z)}Â(z)−P(z){B(z)−{circumflex over (B)}₂(z)}Â(z)  Eq.(56)

[0225] In order to eliminate the unknown number P(z), both equations are arranged as follows: $\begin{array}{cc}P\left(z\right)=\frac{S_1\left(z\right)-\left\{B\left(z\right)-{\hat{B}}_1\left(z\right)\right\}\hat{A}\left(z\right)}{1-\left\{B\left(z\right)-{\hat{B}}_1\left(z\right)\right\}\hat{A}\left(z\right)}& \mathrm{Eq}.\left(57\right)\\ P\left(z\right)=\frac{S_2\left(z\right)-\left\{B\left(z\right)-{\hat{B}}_2\left(z\right)\right\}\hat{A}\left(z\right)}{1-\left\{B\left(z\right)-{\hat{B}}_2\left(z\right)\right\}\hat{A}\left(z\right)}& \mathrm{Eq}.\left(58\right)\end{array}$

[0226] If both are assumed equal, and are arranged for the other unknown number B(z), the following equation can be obtained: $\begin{array}{cc}B\left(z\right)=\frac{S_1\left(z\right)-S_2\left(z\right)+\hat{A}\left(z\right)\left\{{\hat{B}}_1\left(z\right)-{\hat{B}}_2\left(z\right)\right\}+\hat{A}\left(z\right)\left\{S_1\left(z\right){\hat{B}}_2\left(z\right)-S_2\left(z\right){\hat{B}}_1\left(z\right)\right\}}{\hat{A}\left(z\right)\left\{S_1\left(z\right)-S_2\left(z\right)\right\}}& \mathrm{Eq}.\left(59\right)\end{array}$

[0227] As for Eq.(59), in the same way as the case where the schematic arrangement of FIG. 6 is applied to Eq.(46) in the above (3-1), the first filter 121 can only be applied to the numerator and the second filter 122 to the denominator.

[0228] Furthermore, in order to obtain the other unknown number P(z), Eqs.(55) and (56) are arranged as follows: $\begin{array}{cc}B\left(z\right)=\frac{S_1\left(z\right)-P\left(z\right)+{\hat{B}}_1\left(z\right)\hat{A}\left(z\right)\left\{1-P\left(z\right)\right\}}{\hat{A}\left(z\right)\left\{1-P\left(z\right)\right\}}& \mathrm{Eq}.\left(60\right)\\ B\left(z\right)=\frac{S_2\left(z\right)-P\left(z\right)+{\hat{B}}_2\left(z\right)\hat{A}\left(z\right)\left\{1-P\left(z\right)\right\}}{\hat{A}\left(z\right)\left\{1-P\left(z\right)\right\}}& \mathrm{Eq}.\left(61\right)\end{array}$

[0229] By assuming that both are equal, the following equation can be obtained: $\begin{array}{cc}P\left(z\right)=\frac{S_1\left(z\right)-S_2\left(z\right)+\left\{{\hat{B}}_1\left(z\right)-{\hat{B}}_2\left(z\right)\right\}\hat{A}\left(z\right)}{\left\{{\hat{B}}_2\left(z\right)-{\hat{B}}_1\left(z\right)\right\}\hat{A}\left(z\right)}& \mathrm{Eq}.\left(62\right)\end{array}$

[0230] can be obtained.

[0231] When the coefficient of the feedback control filter 210 is not updated with Eq.(59) and the transfer function is maintained to e.g. {circumflex over (B)}₁(z), the coefficient of the noise control filter 220 which cancels the noise x_jto be controlled can be obtained by substituting B(z) and P(z) obtained with Eqs.(59) and (62) for the following equation: $\begin{array}{cc}\hat{A}\left(z\right)=\frac{P\left(z\right)}{\left\{1+P\left(z\right)\right\}B\left(z\right)-{\hat{B}}_1\left(z\right)}& \mathrm{Eq}.\left(63\right)\end{array}$

[0232] in which Eq.(53) is applied to Eq.(38) to be arranged. Also, when the transfer function {circumflex over (B)}₂(z) of the feedback control filter 210 is maintained, the coefficient of the noise control filter 220 which cancels the noise x_jto be controlled is calculated by using the following equation: $\begin{array}{cc}\hat{A}\left(z\right)=\frac{P\left(z\right)}{\left\{1+P\left(z\right)\right\}B\left(z\right)-{\hat{B}}_2\left(z\right)}& \mathrm{Eq}.\left(64\right)\end{array}$

[0233] In addition, when the coefficient of the feedback control filter 210 is updated by using Eq.(59), it is approximated to D(z)=0 in the same way as the above (3-1). Therefore, by using the new transfer function {tilde over (B)}(z) of the feedback control filter 210 calculated from Eq.(59), the following equation can be calculated: $\begin{array}{cc}\hat{A}\left(z\right)=\frac{P\left(z\right)}{\tilde{B}\left(z\right)}& \mathrm{Eq}.\left(65\right)\end{array}$

[0234] Also in this case, like the above (3-1), the coefficients of the noise control filter can be obtained by applying the numerator of Eq.(65) to the first filter 121 and the denominator to the second filter 122.

[0235] It is to be noted that the above-mentioned system identification circuit 120 can be transformed as follows:

[0236] To form the simultaneous equations by using a transfer function provided by the inverse filter composing circuit, from which a constant 1 is removed.

[0237] To form the simultaneous equations by setting the two pairs of fixed coefficients of the noise control filter or the feedback control filter to different taps upon the activation of the apparatus.

[0238] To make the two pairs of coefficients, which are to be set, of the noise control filter or the feedback control filter two pairs of coefficient of the noise control filter or the feedback control filter both set with a time interval.

[0239] To make the two pairs of coefficients, which are to be set, of the noise control filter or the feedback control filter upon the activation of the apparatus coefficients obtained and stored upon the last activation.

[0240] Not to update the coefficient of the feedback control filter when the difference between a new and an old coefficient of the feedback control filter becomes equal to or less than a fixed value upon a coefficient update performed by providing the two pairs of coefficients to the feedback control filter.

[0241] To apply a transfer function corresponding to a coefficient used for the present coefficient update for the two pairs of coefficients, which are to be set, of the noise control filter or the feedback control filter and the transfer function of the inverse filter upon a subsequent coefficient update of the feedback control filter.

[0242] FIG. 1 is a block diagram showing a schematic arrangement of an active noise control apparatus of a feedforward type according to the present invention [1];

[0243] FIG. 2 is a block diagram showing an equivalent structure of a general active noise control apparatus;

[0244] FIG. 3 is a block diagram showing a prior art example in which a white noise generation circuit calculating an error path filter coefficient is not used during an active noise control in a general active noise control apparatus;

[0245] FIG. 4 is a block diagram showing a schematic arrangement of an active noise control apparatus of a feedforward type according to the present invention [2];

[0246] FIG. 5 is a block diagram of an active noise control apparatus which has been proposed in the Japanese Patent Application No.9-239776 (Japanese Patent Publication Laid-open No.11-85165) by the inventors of this invention and others;

[0247] FIG. 6 is a block diagram showing a schematic arrangement of an active noise control apparatus of a feedback type according to the present invention [3];

[0248] FIG. 7 is a block diagram showing an arrangement of an inverse filter circuit by a linear prediction analysis method used for an active noise control apparatus of a feedback type according to the present invention [3];

[0249] FIG. 8 is a block diagram showing an embodiment of an active noise control apparatus according to the present invention [1];

[0250] FIG. 9 is a flow chart showing an operation procedure of an embodiment of an active noise control apparatus according to the present invention [1];

[0251] FIG. 10 is a graph showing a convergence characteristic of a noise control filter coefficient in an active noise control apparatus according to the present invention [1];

[0252] FIG. 11 is a graph of a coefficient estimate of a noise control filter coefficient upon an activation in an active noise control apparatus according to the present invention [1];

[0253] FIG. 12 is a graph for explaining a repeated operation of a coefficient calculation of a noise control filter coefficient in an active noise control apparatus according to the present invention [1];

[0254] FIG. 13 is a block diagram showing an embodiment of a whitening circuit for a colored signal by a linear prediction method used for an active noise control apparatus according to the present invention [2];

[0255] FIG. 14 is a block diagram showing an example of an estimated structure when two coefficients are provided to a noise control filter used for an active noise control apparatus according to the present invention [2];

[0256] FIG. 15 is a simulation graph showing an estimated characteristic of a feedback control filter coefficient upon powering in an active noise control apparatus according to the present invention [2];

[0257] FIG. 16 is a simulation graph showing an example of a convergence characteristic obtained when an initial estimation error is −14 dB and a reducing noise quantity is 20 dB in an active noise control apparatus according to the present invention [2];

[0258] FIG. 17 is a flow chart showing a procedure example of performing a coefficient update of a feedback control filter by setting two pairs of independent coefficients in a noise control filter in an active noise control apparatus according to the present invention [2];

[0259] FIG. 18 is a simulation graph showing an estimated characteristic when a primary noise is a colored noise and the number of taps of a non-recursive filter (111)=the number of taps of a feedback control filter+the number of taps of a noise control filter+a generation process degree of a primary noise in an active noise control apparatus according to the present invention [2];

[0260] FIG. 19 is a simulation graph showing an estimated characteristic when a primary noise is a colored noise and the number of taps of a non-recursive filter (111) is elongated in an active noise control apparatus according to the present invention [2];

[0261] FIG. 20 is a simulation graph showing an estimated characteristic when a primary noise is a colored noise and the number of taps of a non-recursive filter (111)=the number of taps of a feedback control filter+the number of taps of a noise control filter in an active noise control apparatus according to the present invention [2];

[0262] FIG. 21 is a block diagram showing an example of an estimate structure when two coefficients are provided to a feedback control filter in an active noise control apparatus according to the present invention [2];

[0263] FIG. 22 is a simulation graph showing an estimated characteristic when two pairs of coefficients having an estimation error −14 dB are provided to a feedback control filter in an active noise control apparatus according to the present invention [2];

[0264] FIG. 23 is a flow chart showing a procedure example for estimating an impulse response of a feedback path by setting two pairs of independent coefficients in a feedback control filter in an active noise control apparatus according to the present invention [2];

[0265] FIG. 24 is a block diagram showing an embodiment of a circuit which identifies a difference between transfer functions of a feedback path and a feedback control filter by providing two pairs of coefficients to a noise control filter used for an active noise control apparatus of a feedback type according to the present invention [3];

[0266] FIG. 25 is a block diagram showing an embodiment of a circuit which identifies a coefficient of a noise control filter which optimally cancels a primary noise by providing two pairs of coefficients to a noise control filter used for an active noise control apparatus of a feedback type according to the present invention [3];

[0267] FIG. 26 is a block diagram showing an embodiment of a circuit which identifies a characteristic of a feedback path by providing two pairs of coefficients to a feedback control filter used for an active noise control apparatus of a feedback type according to the present invention [3];

[0268] FIG. 27 is a block diagram showing an embodiment of a circuit which identifies a coefficient of a noise control filter which optimally cancels a primary noise by providing two pairs of coefficients to a feedback control filter used for an active noise control apparatus of a feedback type according to the present invention [3];

[0269] FIG. 28 is a flow chart showing a procedure of performing a coefficient update of a feedback control filter and a noise control filter by setting two pairs of independent coefficients to a noise control filter in an active noise control apparatus of a feedback type according to the present invention [3];

[0270] FIG. 29 is a flow chart showing a procedure of performing a coefficient update of a feedback control filter and a noise control filter by setting two pairs of independent coefficients in a feedback control filter in an active noise control apparatus of a feedback type according to the present invention [3];

[0271] FIG. 30 is a block diagram showing an arrangement of a general active noise control apparatus;

[0272] FIG. 31 is a block diagram showing a calculation circuit of an error path filter coefficient in a general active noise control apparatus;

[0273] FIG. 32 is a block diagram showing a prior art example for calculating an error path filter coefficient during an active noise control in a general active noise control apparatus;

[0274] FIG. 33 is a block diagram showing an example of a general calculation circuit of a feedback control filter coefficient used before starting a noise control;

[0275] FIG. 34 is a block diagram showing a prior art example of an active noise control apparatus for performing an update of a feedback control filter coefficient during an active noise control;

[0276] FIG. 35 is a block diagram showing an example of a circuit arrangement of a generally known active noise control apparatus of a feedback type;

[0277] FIG. 36 is a block diagram showing a circuit arrangement for calculating a coefficient of a feedback control filter used for a generally known active noise control apparatus of a feedback type;

[0278] FIG. 37 is a block diagram equivalently showing a generally known active noise control apparatus of a feedback type;

[0279] FIG. 38 is a block diagram showing a generally known active noise control apparatus of a feedback type of an adaptive prediction type; and

[0280] FIG. 39 is a block diagram equivalently showing a prediction part of a generally known active noise control apparatus of a feedback type of an adaptive prediction type.

[0281] Throughout the figures, like reference numerals indicate like or corresponding components.

[0282] FIG. 8 shows an embodiment of an active noise control apparatus according to the present invention [1]. This embodiment is composed of a duct 200 as a noise transmission system, a noise detecting microphone 201 for detecting a noise flowing through the duct 200, an error detecting microphone 202 provided at an outlet end of the duct 200, a loud speaker 203, provided oppositely to the microphone 202, for outputting a secondary noise to the duct 200, and a computer 300 for generating the secondary noise provided to the loud speaker 203 based on a noise signal detected at the microphone 201 and an error signal detected at the microphone 202.

[0283] FIG. 9 is a flow chart of a simulation process in the above-mentioned computer 300 for confirming the effectiveness of the active noise control apparatus according to the present invention whose principle is shown in FIG. 1. The operation of the embodiment of the present invention shown in FIG. 8 will be described by referring to this flow chart and the arrangements of FIGS. 1-3.

[0284] FIG. 10 is a graph showing a simulation result for confirming the effectiveness of the active noise control apparatus according to the present invention on a relationship between a coefficient updating frequency and an estimation error.

[0285] For the first and the second coefficient A₁and A₂to be provided to the noise control filter, the following equations:

[0286] w₁=[w₁(1)w₁(2) . . . w₁(I)]  Eq.(66)

[0287] w₂=[w₂(1)w₂(2) . . . w₂(I)]  Eq.(67)

[0288] consisting of 2I sampled values of the white noise whose average amplitude assumes e.g. {fraction (1/10)} of an impulse response D, are added to the impulse response D of the duct 200 to obtain A₁and A₂as follows:

[0289] A₁[D(1)+w₁(1)D(2)+w₁(2) . . . D(I)+w₁(I)]  Eq.(68)

[0290] A₂[D(1)+w₂(1)D(2)+w₂(2) . . . D(I)+w₂(I)]  Eq.(69)

[0291] It is adapted that the power ratio of the noise G_jand a turbulence from the outside of the duct 200 is 40 dB, an NLMS algorithm is used for the coefficient updating algorithm of the overall system filter 260 where the step gain is made 0.01, and the coefficient updating frequency of the overall system filter 260 is stopped by 2500 times. Also, the length of the impulse response D of the error path 190 and the duct 200 is made 128.

[0292] From the simulation result of FIG. 10, it is confirmed that the impulse response D of the duct 200 is calculated as the coefficient of the estimating noise transfer system filter 147 according to this embodiment.

[0293] On the other hand, upon the initial activation of this active noise control apparatus, the coefficient of the noise control filter 220 has not been estimated yet. Accordingly, it can be arbitrarily set. The easiest setting method is that A₁=0 is provided for the coefficient of the first noise control filter 144 within the noise control filter 220 (at step T1 of FIG. 9). With the coefficient A₁, the coefficient S₁of the first overall system filter 141 can be estimated from the arrangement of FIG. 3 (at step T2).

[0294] Also, for the coefficient of the second noise control filter 142, a constant “a” is provided only to a single proper tap.

[0295] For instance, it is supposed (at step T3) that:

[0296] A₂=[a0 . . . 0]  Eq.(70)

[0297] With this coefficient A₂, the coefficient S₂of the second overall system filter 142 can be estimated from the arrangement of FIG. 3 (at step T4).

[0298] As a result, since the above-mentioned Eq.(13) simply assumes

[0299] D=S₁a/(S₁−S₂)  Eq.(71)

[0300] Therefore, the coefficient of the estimating noise transfer system filter 147 is to provide the impulse response D of the duct 200 (at step T5), if the calculation is similarly performed by applying A₁=0 and the present (latest) coefficient A₂of Eq.(70) to the principle of the present invention shown in FIG. 1.

[0301] FIG. 11 is a graph showing the result of the simulation for confirming that the impulse response of the duct 200 is calculated for the coefficient of the estimating noise transfer system filter 147 by the coefficient setting as mentioned above, on the relationship between the coefficient updating frequency and the estimation error in the same way as FIG. 10. However, in this case, compared with the condition provided to FIG. 10, they are different in that the step gain of the NLMS algorithm of performing the coefficient update of the overall system filter 260 is changed into 0.1.

[0302] Also, for the first element of the coefficient A₂of Eq.(70), “a=1” is set. That an arbitrary coefficient can be set for the coefficient of the noise control filter 220 in this way leads to that the noise of the active noise control apparatus can be suppressed small from the beginning of the activation if the apparatus is arranged such that the coefficients A₁and A₂of the first and the second noise control filter 144 and 142 forming the noise control filter 220 whose noise is preliminarily estimated and reduced are preliminarily stored in a memory (not shown) within the computer 300, they are read upon the activation to be applied to the embodiment, and the impulse response of the duct 200 is calculated.

[0303] The update method after calculating the coefficients A₁and A₂of the noise control filter 220 as mentioned above and activating the noise control will be described.

[0304] The coefficient estimation error of the noise control filter 220 calculated according to the principle of the present invention corresponds to the estimation error after the convergence of the coefficients S₁and S₂of the first and the second overall system filter 141 and 143 forming the overall system filter 260. It is known that this estimation error is approximated to a white noise w₁as given by the following equation:

[0305] A₁=[D(1)+w₁(1)D(2)+w₁(2) . . . D(I)+w₁(1)]  Eq.(72)

[0306] “I” number of sampled values, obtained from the white noise generation circuit 250,

[0307] w=[w(1)w(2) . . . w(I)]  Eq.(73)

[0308] are added to the present coefficient A₁of the noise control filter 220 to obtain the following equation:

[0309] A₂=[A₁(1)+w(1)A₁(2)+w(2) . . . A₁(I)+w(I)]  Eq.(74)

[0310] If the above Eq.(72) is substituted for Eq.(74), the following equation can be obtained:

[0311] A₂=[D(1)+w₁(1)+w(1)D(2)+w₁(2)+w(2) . . . D(I)+w₁(I)+w(I)]  Eq.(75)

[0312] Obviously, this coefficient A₂corresponds to the case where the following equation is assumed:

[0313] w₂=[w₁(1)+w(1)w₁(2)+w(2)w₁(I)+w(I)]  Eq.(76)

[0314] Also at this time, the coefficient of the noise control filter 220 can be calculated by the circuit of FIG. 1.

[0315] In this case, the coefficient estimation error of the noise control filter 220 calculated according to the principle of the present invention corresponds to the estimation error after the convergence of the coefficient of the overall system filter 260. Since it is approximated to the white noise as mentioned above, the operation of adding “I” number of sampled values obtained from the white noise generation circuit 250 to the present coefficient A₁is equal to the decrease of the noise canceling quantity.

[0316] This is the different point from the prior art active noise control apparatus in which the white noise is overlapped and a different kinds of noise is transmitted from the duct 200. The different kind of noise is easy to be detected even if it is small.

[0317] Nevertheless, the operation of decreasing the noise canceling quantity is not preferable, and it is naturally preferable that the reduction quantity is little. In addition, it is imagined that actually the characteristic of each acoustic system continuously changes.

[0318] Accordingly, the coefficient of the noise control filter 220 is required to be repeatedly updated. At this time, there are two coefficients obtained as the result of the last and the present coefficient update. The estimation errors are included in the two coefficients. The estimation errors are regarded as the coefficients A₁and A₂having the following errors for the impulse response of the present accurate duct 200:

[0319] A₁=[D(1)+w₁(1)D(2)+w₁(2) . . . D(I)+w₁(I)]  Eq.(77)

[0320] A₂=[D(1)+w₂(1)D(2)+w₂(2) . . . D(I)+w₂(I)]  Eq.(78)

[0321] With these equations, the coefficient of the estimating noise transfer system filter 147 is to be obtained according to the principle of the present invention.

[0322] In FIG. 12, the coefficient of the noise control filter calculated by assuming A₁=0 and a=1 for the first element of the coefficient A₂provided to Eq.(70) upon the activation is used again, the last A₂is used for A₁, (i.e. A₁=A₂, and A₂is replaced with the coefficient calculated presently (this time). The coefficient of the estimating noise transfer system filter 147 when such an operation is repeated has a convergence characteristic. This is similarly performed to the coefficients S₁and S₂of the overall system filter (at step T6).

[0323] Then, the obtained impulse response D is made the latest coefficient A₂(at step T7), at which above-mentioned steps T4-T7, at which the coefficient S₂is obtained and the impulse response D is further estimated, are repeated.

[0324] From FIG. 12, it is seen that the impulse response of the duct 200 is accurately estimated according to the principle of the present invention [1] except that a convergence value of the coefficient estimation error of the noise control filter 220 becomes large at the second time and the following.

[0325] Also, according to Eq.(9), the output of the overall system filter 260 whose coefficient is converged is not canceled by the secondary noise synthesized by the noise control filter 220 but is approximated to the noise left. Namely, the ratio of the output of the noise control filter 220 and the output of the overall system filter 260 corresponds to the canceled quantity of the noise achieved by this apparatus.

[0326] On the other hand, when the fixed-point arithmetic by which the actual active noise control apparatus can be inexpensively manufactured is adopted, there is a limit in the canceled quantity of the noise which can be realized under the restriction of a dynamic range.

[0327] Therefore, it is an actual measure that the canceled quantity to be achieved is predetermined, the operation of updating the coefficient of the noise control filter 220 is stopped when the above-mentioned ratio achieves the canceled quantity, and the coefficient is updated only when the canceled quantity becomes equal to or less than a threshold value.

[0328] Of course, since the output of the overall system filter 260 indicates the magnitude of the noise which has been left uncanceled, it becomes possible to control the stop/start of the coefficient update even by referring not to the above-mentioned ratio but only to the output of the overall system filter 260.

[0329] Thus, the active noise control apparatus according to the present invention [1] is arranged such that an overall system filter which simulates a characteristic of an overall system leading to an error detecting microphone from a noise detecting microphone is provided as a first and a second overall system filter, and a second and a first noise control filter forming a noise control filter are connected to the first and the second overall system filter in cascade, and the coefficient of the estimating noise transfer system filter is made coefficients of the noise control filters when a difference between the differential output between both when the white noise is applied to the circuit of the cascade combination, and a difference between the response of the first and the second overall system filter from the differential overall system filter becomes a minimum. Therefore, the coefficient of the noise control filter can be updated without transmitting the white noise from the loud speaker during the active noise control and without calculating the coefficient of the error path filter.

[0330] The present invention [2] will be specifically described by referring to an example where a feedback control filter and a noise control filter are composed of a non-recursive filter which is often used for an active noise control apparatus. In addition, the inverse filter composing circuit 110 is composed such that the coefficient of the non-recursive filter 111 for inputting the colored signal as shown in FIG. 13 is updated at the coefficient updating circuit 112 to obtain a white signal from the subtracter 113.

[0331] In this case, the transfer function of the non-recursive filter 111 in FIG. 13 assumes

[0332] S(z)=1−X⁻¹(z)  Eq.(79)

[0333] upon the convergence of the coefficient, and

[0334] S(z)=P(z)+D(z)A(z)−P(z)D(z)A(z)  Eq.(80)

[0335] can be obtained.

[0336] Accordingly, the embodiment will be described by using the following equation in which Eqs.(26) and (34) are applied to Eq.(80): $\begin{array}{cc}D\left(z\right)=\frac{S_1\left(z\right)-S_2\left(z\right)}{A_1\left(z\right)\left\{1-S_2\left(z\right)\right\}-A_2\left(z\right)\left\{1-S_1\left(z\right)\right\}}B\left(z\right)=\frac{S_1\left(z\right)-S_2\left(z\right)+A\left(z\right)\left\{{\hat{B}}_1\left(z\right)-{\hat{B}}_2\left(z\right)\right\}+A\left(z\right)\left\{S_1\left(z\right){\hat{B}}_2\left(z\right)-S_2\left(z\right){\hat{B}}_1\left(z\right)\right\}}{A\left(z\right)\left\{S_1\left(z\right)-S_2\left(z\right)\right\}}& \mathrm{Eq}.\left(81\right)\end{array}$

[0337] This is equal to making the simultaneous equations by adding the transformation of Eq.(79) to the transfer function of the inverse filter formed within the inverse filter composing circuit 110.

[0338] (2-1) Embodiment in Case of Providing Two Pairs of Fixed Coefficients to Noise Control Filter 220:

[0339] If two pairs of coefficients are set in the noise control filter 220 and the transfer functions A₁(z), A₂(z), S₁(z), S₂(z) defined by Eq.(80) obtained at the inverse filter composing circuit 110 are formed by using supplemental filters 2141, 2142, 2131, 2132, and subtracters 2133-2135, 2143, and 151, as well as an adaptive filter 150 as shown in FIG. 14, the subtracter 151 provides the difference between S₁(z)−S₂(z) and [A₁(z){1−S₂(z)}−A₂(z){1−S₁(z)}]d(z) corresponding to Eq.(81).

[0340] Accordingly, if the transfer function d(z) of the adaptive filter 150 is composed of the non-recursive filter, and the coefficient

[0341] d=[d(1)d(2) . . . d(I)]^T  Eq.(83)

[0342] is updated by using a method such as an NLMS algorithm in order that the output of the subtracter 151 may become the minimum, the coefficient “d” of the transfer function d(z) of the adaptive filter 150 converges into the impulse response corresponding to the transfer function D(z) when it reaches the minimum.

[0343] Assuming the coefficients of the feedback control filter 210 formed by the impulse response of the feedback path and the non-recursive filter are respectively

[0344] B=[B(1)B(2) . . . B(I)]^T  Eq.(84)

[0345] {circumflex over (B)}=[{circumflex over (B)}(1){circumflex over (B)}(2) . . . {circumflex over (B)}(I)]^T  Eq.(85)

[0346] the coefficient “d” converges into the following equation:

[0347] D=[D(1)D(2) . . . D(I)]^T=[B(1)−{circumflex over (B)}(1)B(2)−{circumflex over (B)}(2) . . . B(I)−{circumflex over (B)}(I)]^T  Eq.(86)

[0348] According to Eq.(86), it is obviously seen that adding the difference D to the coefficient {circumflex over (B)}(z) of the feedback control filter 210 provides such an effect that the coefficient {circumflex over (B)}(z) is approximated to the impulse response “B” of the feedback path in this embodiment.

[0349] FIG. 15 is the result of the simulation performed for confirming that the present invention effectively operates just after the power activation. The problem just after the power activation is that the coefficients of the feedback control filter 210 and the noise control filter 220 have not been calculated yet.

[0350] Since the present invention does not operate when the above-mentioned closed circuit is not formed with the both filters, it is necessary to set the coefficients in the both filters.

[0351] However, if the coefficients are set, then the closed circuit is formed, so that at that moment a danger of a howling occurrence is generated. For this reason, the selection of both coefficients is required carefully so as not to generate the howling.

[0352] In this example,

[0353] {circumflex over (B)}=0  Eq.(87)

[0354] is set in the feedback control filter 210. This coefficient does not increase the gain of the closed circuit more than now.

[0355] The coefficient of the noise control filter 220 has been calculated, neither.

[0356] However, for the coefficient of the filter 220, “A=0” can not be set. This is because the transmission of the secondary noise from the loud speaker 203 is required for calculating the coefficient of the feedback control filter 210. At the same time, since it is required that the fixed coefficients A₁and A₂of the set noise control filter 220 compose two independent inverse filters for the inverse filter composing circuit 110, the following equation:

[0357] A₁^TA₂=0  Eq.(88)

[0358] is required to be satisfied.

[0359] In this embodiment, for the coefficient to satisfy Eq.(88),

[0360] A₁=[a0 . . . 0]  Eq.(89)

[0361] A₁=[00 . . . a]  Eq.(90)

[0362] are selected, so that 0.2 is provided for a constant “a” in the example of FIG. 15.

[0363] Also, it is assumed in this example that the tap numbers of the noise control filter 220 and the feedback control filter 210 are both 128, the primary noise is the white noise, the tap number of the non-recursive filter 111 in FIG. 13 for obtaining the transfer functions S₁(z) and S₂(z) is 256, the NLMS algorithm is used in which the step gain is 0.000125 in the algorithm for updating the coefficient, and the coefficient updating frequency is 2,048×128×64=16,777,216.

[0364] The abscissa of FIG. 15 denotes the coefficient updating frequency of the adaptive filter 150. The result of the simulation in FIG. 15 shows that as the coefficient update goes on, the estimation error decreases and is made stable in the vicinity of −25 dB, so that the effectiveness of the method according to the present invention by which the coefficient of the noise control filter 220 is provided as Eqs.(89) and (90) is demonstrated.

[0365] As mentioned above, the object of the present invention [2] is to update the coefficient of the feedback control filter 210 during the noise control according to the characteristic change of the feedback path. In order to achieve this object, two independent equations are required.

[0366] It is available that the coefficient of the noise control filter 220 is not be actually obtained because of zero error.

[0367] Namely, the error left after the convergence of the coefficient of the noise control filter 220 is regarded as Gaussian white noise, so that the error (difference) between the fixed coefficients A₁and A₂obtained by stopping the coefficient update with a time interval after the convergence provides mutually independent noises.

[0368] The coefficient update of the feedback control filter 210 during the noise control can be performed by using the coefficients A₁and A₂having such an independent error.

[0369] FIG. 16 shows the result of the simulation assuming that the coefficient of the feedback control filter 210 is obtained with the initial estimation error being −14 dB for the impulse response of the feedback path by the last coefficient update, and the noise canceling quantity of 20 dB (corresponding to the estimation error −20 dB of coefficient of noise control filter 220) is obtained

[0370] Namely, two pairs of signal vectors are prepared by the white primary noise whose power ratio to the impulse response of the feedback path is −20 dB, and added to the impulse response of the feedback path to calculate the fixed coefficients A₁and A₂.

[0371] Also, it is assumed that the coefficient updating frequency of the non-recursive filter 111 in FIG. 13 for obtaining the transfer functions S₁(z) and S₂(z) is 2,048×128×80=20,971,520, the step gain is 0.000125, and the other conditions are the same as FIG. 15.

[0372] From this result, the effectiveness of taking advantage of the independence of the error left in the coefficient of the noise control filter 220 can be confirmed.

[0373] This simultaneously indicates that the coefficient of the feedback control filter 210 can be calculated as mentioned above by such an arrangement that the coefficients of the noise control filter 220 and the feedback control filter 210 obtained during the last power activation are preliminarily stored in the memory (not shown), and upon the present power activation the stored coefficients are set in both filters.

[0374] Taking advantage of these stored coefficients, the effect of the active noise control can be obtained from the beginning of power activation in such a system where the acoustic system characteristic is relatively stable.

[0375] If the feedback control filter 210 thus simulates the feedback path well by the effect of the present invention, a feedback component ratio included in the output of the subtracter 204 used for the composition of the inverse filter decreases, so that the calculation accuracy of the transfer function S(z) deteriorates. The deterioration further deteriorates the calculation accuracy of the coefficient of the feedback control filter 210.

[0376] The deterioration can be prevented by lessening the step gain gradually according to the decrease, as performed in the example of FIG. 16 where the feedback component ratio included in the output of the subtracter 204 is small as compared with that of FIG. 15.

[0377] However, it is not actually necessary that the calculation accuracy of the coefficient of the feedback control filter 210 is raised infinitely. It is enough that the update of the coefficient is stopped when accuracy more than a fixed one is secured and the update is restarted when the accuracy deteriorates.

[0378] The accuracy obtained by the present coefficient update can be anticipated from the gain of the adaptive filter 150 upon the convergence of the coefficient of the adaptive filter 150, as seen from the fact that the transfer function of the adaptive filter 150 provides the difference D(z) between the transfer functions of the feedback path and the feedback control filter 210.

[0379] Namely, by monitoring a gain G of the adaptive filter 150 and updating the coefficient of the feedback control filter 210 only when the gain G is equal to or more than a predetermined gain G₀, such a disadvantage can be removed that the improvement of the calculation accuracy of the coefficient of the feedback control filter 210 causes the deterioration again.

[0380] FIG. 17 is a flow chart showing the operation from the power activation when two pairs of fixed coefficients are set in the noise control filter 220 to update the coefficient of the feedback control filter 210.

[0381] In this flow chart, for the process upon the power activation, the above-mentioned Eq.(87) is firstly set (at step T11), and the coefficient A₁of the noise control filter 220 is set as Eq.(89) (at step T12). Thus, the coefficient S₁can be calculated. (at step T13).

[0382] By setting the coefficient A₁in the noise control filter 220, a part of the coefficients of the non-recursive filter 111 in FIG. 13 is to be set, so that the coefficient updating circuit 112 converges the coefficient update of the filter 220 in order that the outputted white noise signal (w_j) may become the minimum. At this time, the coefficient of the filter 111 assumes S₁.

[0383] Furthermore, by setting the coefficient A₂with Eq.(90) (at step T14), the coefficient S₂is similarly calculated (at step T5).

[0384] Then, as mentioned above, the gain G of the adaptive filter 150 is monitored (at step T16) to perform the coefficient update of the feedback control filter 210 only when the gain is equal to or more than the predetermined value G₀(at step T17). Then, the coefficients S₂and A₂obtained are respectively replaced with the coefficients S₁and A₁(at steps T18 and T19), and the new coefficient A₂is set for the second coefficient update (at step T20). The routine then proceeds to step T5 and the following steps.

[0385] Namely, in this flow chart, among the two pairs of fixed coefficients A₁and A₂of the noise control filter 220 and the coefficients S₁and S₂, of the inverse filter used for the first coefficient update of the feedback control filter 210 after the power activation, the latest coefficients are utilized for the subsequent coefficient update as they are. That the coefficient can be utilized in such a way is obvious from the fact that the error left in the coefficient of the noise control filter 220 is regarded as an independent noise.

[0386] FIG. 18 is the result of the simulation performed by supposing that the primary noise comprises a colored noise. For the colored noise, the output obtained by applying the white noise to the second recursive filter 1/(1−1.4 cos 0.25πz⁻¹1+0.49z⁻²is provided.

[0387] Moreover, the NLMS algorithm is used in which it is assumed that the number of taps of the non-recursive filter 111 of FIG. 13 which provides the transfer functions S₁(z) and S₂(z) is 258, the step gain is 0.0001, so that the coefficient updating frequency is 2,048×128×200=52,428,800. The other conditions are the same as the example of FIG. 16. From this result, it is confirmed that the present invention operates effectively when the primary noise comprise a colored noise.

[0388] Generally, the degree of the generation process of the primary noise can not be known beforehand. In such a case, there is a possibility that the number of taps of the non-recursive filter 111 in FIG. 13 which provides the transfer functions S₁(z) and S₂(z) comprises larger than is necessary.

[0389] FIG. 19 is a simulation result performed for confirming that the present invention effectively operates in such a case.

[0390] It is assumed that the number of taps of the non-recursive filter 111 in FIG. 13 which provides the transfer functions S₁(z) and S₂(z) is 384 large enough, the step gain is 0.0001, the coefficient updating frequency is 2,048×128×200=52,428,800, and the other conditions are provided in the same way as the conditions of FIG. 18.

[0391] On the other hand, FIG. 20 shows a result in the case that the degree of the generation process P(z) of the primary noise is estimated to be “0”. It is similarly assumed that the number of taps of the non-recursive filter 111 in FIG. 13 which provides the transfer functions S₁(z) and S₂(z) is 256, the step gain is 0.0001, the coefficient updating frequency is 2,048×128×200=52,428,800, and the other conditions are set in the same way as the conditions of FIG. 18.

[0392] The results shown in FIGS. 19 and 20 indicate that even if the degree of the generation process of the primary noise is not accurately estimated, the present invention effectively operates.

[0393] (2-2) Embodiment in Case of Providing Two Pairs of Fixed Coefficients to Feedback Control Filter 210:

[0394] From the transfer function of the inverse filter obtained when two pairs of independent fixed coefficients are provided to the feedback control filter 210, the impulse response of the feedback path can be estimated by developing Eq.(82) into the system identification circuit, by subsidiary filters 2131, 2132, 2144-2147, subtracters 2136-2139, 151, and the adaptive filter 150 as shown in FIG. 21.

[0395] In this case, different from the case where two pairs of independent fixed coefficients are provided to the noise control filter 220, the coefficient of the adaptive filter 150 provides the impulse response B of the feedback path upon the convergence. Accordingly, the coefficient update of the feedback control filter 210 is performed by exchanging the coefficients of the adaptive filter 150 and the feedback control filter 210.

[0396] FIG. 22 shows the result of the simulation which has confirmed the effectiveness of the present invention by providing a single pair of fixed coefficients to the noise control filter 220 and by providing two pairs of independent fixed coefficients to the feedback control filter 210. Two pairs of independent fixed coefficients whose error with the feedback path is −14 dB are provided to the feedback control filter 210.

[0397] It is also assumed that the number of taps of the non-recursive filter 111 in FIG. 13 which provides the transfer functions S₁(z) and S₂(z) is 256, the step gain is 0.0001, the coefficient updating frequency is 2,048×128×100=26,214,400, and the other conditions are set in the same way as the conditions of FIG. 18.

[0398] From this result, it is confirmed that the impulse response of the feedback path in the present invention is estimated as the coefficient of the adaptive filter.

[0399] FIG. 23 shows a flow chart for setting two pairs of fixed coefficients to the feedback control filter 220, and for calculating the impulse response of the feedback path from two inverse filters formed for each of the coefficients as the coefficients of the adaptive filter.

[0400] Firstly, upon the power activation, the coefficients of the feedback control filter 210 and the noise control filter 220 have not been set yet.

[0401] Therefore, the coefficient

[0402] Â=[a0 . . . 0]  Eq.(91)

[0403] is set in the noise control filter 220 (at step T21).

[0404] The constant should be determined to the extent that the noise increase by the secondary noise transmitted from the loud speaker 203 may not become extremely large. Also, for two pairs of independent fixed coefficients set in the feedback control filter 210 for satisfying

[0405] {circumflex over (B)}₁^T{circumflex over (B)}₂=0  Eq.(92)

[0406] the following equations are set (at steps T22 and T24):

[0407] {circumflex over (B)}₁=0  Eq.(93)

[0408] {circumflex over (B)}₂=[b0 . . . 0]  Eq.(94)

[0409] It is necessary that such a small value as does not generate the howling is selected to be set to the constant “c”. It is to be noted that the calculation of the coefficients S₁and S₂is the same as the case of FIG. 17 (at steps T23 and T25).

[0410] In this flow chart, after the power activation, the two pairs of coefficients of the feedback control filter 210 are obtained, so that when the impulse response of the feedback path is estimated, a single pair of coefficients set upon the last update and the obtained coefficient of the inverse filter are utilized upon the subsequent coefficient update as they are (at steps T27-T29). This is the same method as the above-mentioned method for providing two pairs of coefficients of the noise control filter 220.

[0411] Moreover, the output of the non-recursive filter 111 in FIG. 13 is composed of the correlation component forming the controlled noise and the recursive component included in the output of the subtracter 204, in which the time when the output P becomes equal to or less than a fixed value is the time when the recursive component becomes equal to or less than a fixed value (at step T26). It means that the gain of the closed circuit becomes equal to or less than a fixed value P₀, so that the necessity of updating the coefficient of the feedback control filter 210 is lessened. Therefore, the flow chart of FIG. 23 is formed so that steps T26→T25 are repeated, and the update is interrupted.

[0412] As described above, according to an active noise control apparatus according to the present invention [2] is arranged such that an inverse filter composing circuit forms a filter having a characteristic including a transfer function opposite to a closed circuit starting from the noise control filter and returning to the noise control filter again through both of the feedback path and the feedback control filter, the transfer function expressing a generation process of the primary noise, and a system identification circuit provides two pairs of different fixed coefficients either to the feedback control filter or the noise control filter to update a coefficient of an adaptive filter in order that a difference becomes a minimum between a numerator of a solution obtained by eliminating a transfer function component expressing the generation process of the primary noise, from simultaneous equations based on two transfer functions of an inverse filter formed within the inverse filter composing circuit for the two pairs of coefficients and an output of the adaptive filter connected to a denominator of the solution, and a coefficient of the feedback control filter is updated by using the coefficient of the adaptive filter obtained by operating the system identification circuit. Therefore, the coefficient of the feedback control filter can be updated without outputting the white noise from the loud speaker during the active noise control.

[0413] The embodiment of an active noise control apparatus of a feedback type according to the present invention [3] will now be described.

[0414] Firstly, the above-mentioned transfer function Â(z) should be actually obtained for the coefficient of the filter. The example of calculating the coefficient of the noise control filter 220 with the structure of the all filters being made a non-recursive type will be specifically described. It is now available that the coefficient of the non-recursive filter coincides with the impulse response, and the product of the transfer function corresponds to a convolution operation in the time domain.

[0415] (3-1) Embodiment in Case of Providing Two Pairs of Coefficients to Noise Control Filter:

[0416] Firstly, the denominator on the right side of Eq.(46) is canceled and

[0417] [A₁(z){1−S₂(z)}−A₂(z){1−S₁(z)}]D(z)=S₁(z)−S₂(z)  Eq.(95)

[0418] is obtained. The system identification circuit 120 shown in FIG. 24 is composed by combining the filters whose transfer functions are the known A₁(z), A₂(z), S₁(z), and S₂(z) and the adaptive filter d(z).

[0419] Namely, the first filter 121 shown in FIG. 6 is composed of filters 1211, 1212 and a subtracter 1213, and the second filter 122 is composed of filters 1221-1224 and subtracters 1225-1227.

[0420] If the coefficient d(z) of the adaptive filter 123 is updated in order that the output of the subtracter 1227 [A₁(z){1−S₂(z)}A₁(z)−A₂(z){1−S₁(z)}] and the output of the subtracter 1213 {S₁(z)−S₂(z)} may become mutually equal, i.e. the output of the subtracter 124 may become “0” in the system identification circuit 120, the transfer function d(z) of the adaptive filter 123 coincides with the transfer function D(z) when the coefficient d(z) has converged.

[0421] Since the adaptive filter 123 is composed of the non-recursive filter in this embodiment, the coefficient

[0422] d=[d(1)d(2) . . . d(I)]^T  Eq.(96)

[0423] provides the difference between the following impulse response of the feedback path

[0424] B=[B(1)B(2) . . . B(I)]^T  Eq.(97)

[0425] and the following coefficient of the feedback control filter 210

[0426] {circumflex over (B)}=[{circumflex over (B)}(1){circumflex over (B)}(2) . . . {circumflex over (B)}(I)]^T  Eq.(98)

[0427] Namely, by adding the coefficient “d” of the adaptive filter 123 to the present coefficient {circumflex over (B)} of the feedback control filter 210, $\begin{array}{cc}\begin{array}{c}\tilde{B}=\hat{B}+d\\ ={\left[\begin{array}{cccc}\hat{B}\left(1\right)& \hat{B}\left(2\right)& \cdots & \hat{B}\left(1\right)\end{array}\right]}^T+\\ {\left[\begin{array}{cccc}B\left(1\right)-\hat{B}\left(1\right)& B\left(2\right)-\hat{B}\left(2\right)& \cdots & B\left(1\right)-\hat{B}\left(1\right)\end{array}\right]}^T\\ =B\end{array}& \mathrm{Eq}.\left(99\right)\end{array}$

[0428] is obtained, so that the coefficient of the feedback control filter 210 is to obtain the coefficient approximated to the impulse response B of the feedback path.

[0429] When the coefficient of the feedback control filter 210 is thus updated, D(z) is approximated to null from Eq.(39), so that the coefficient of the noise control filter 220 which optimally reduces the noise x_jto be controlled can be calculated with Eq.(52).

[0430] Eq.(52) is applied to Eq.(49) to be transformed as follows:

[0431] {circumflex over (B)}(z){A₁(z)−A₂(z)}Â(z)=S₂(z)A₁(z)−S₁(z)A₂(z)  Eq.(100)

[0432] The adaptive filter a(z) is introduced instead of the transfer function Â(z) to form the system identification circuit 120 shown in FIG. 25.

[0433] Namely, in this system identification circuit 120, the filters 1211, 1212, 1214, 1215 and the subtracter 1213 compose the first filter 121, and the filters 1223, 1224, 1228 and the subtracter 1227 compose the second filter 122.

[0434] When the coefficient of the adaptive filter a(z) has converged in this composition, the following coefficient

[0435] a=[a(1)a(2) . . . a(I)]^T  Eq.(101)

[0436] provides the following coefficient of the noise control filter 220

[0437] Â=[Â(1)Â(2) . . . Â(I)]^T  Eq.(102)

[0438] which optimally reduces the object noise x_jto be controlled.

[0439] (3-2) Embodiment in Case of Providing Two Pairs of Coefficients to Feedback Control Filter:

[0440] In this case, the transfer function of the feedback path can be directly obtained. The denominator on the right side of Eq.(59) is canceled and

[0441] B(z)Â(z){S₁(z)−S₂(z)}=S₁(z)−S₂(z)+Â(z)[{circumflex over (B)}₁(z){1−S₂(z)}−{circumflex over (B)}₂(z){1−S₁(z)}]  Eq.(103)

[0442] is obtained. Then, an adaptive filter b(z) is introduced to form the system identification circuit of FIG. 26.

[0443] Namely, filters 1211, 1212, 1216, 1217, 12110, 12111, 12113, and subtracters 1213, 1218, 1219, 12112, and 12114 compose the first filter 121, and filters 1221, 1222, 1229 and the subtracter 1227 compose the second filter 122.

[0444] When the coefficient of the adaptive filter (b(z)) 123 has converged in this composition, the estimated value of the impulse response of the feedback path

[0445] {tilde over (B)}=[{tilde over (B)}(1){tilde over (B)}(2) . . . {tilde over (B)}(I)]  Eq.(104)

[0446] can be obtained.

[0447] Accordingly, if the system identification circuit 120 of

[0448] {{circumflex over (B)}₂(z)−{circumflex over (B)}₁(z)}Â(z){tilde over (B)}(z)a(z)=S₁(z)−S₂(z)+{{circumflex over (B)}₁(z)−{circumflex over (B)}₂(z)}Â(z)  Eq.(105)

[0449] where Eq.(62) is applied to Eq.(65) to be arranged with Eq.(104), as shown in FIG. 27, is composed of the first filter 121 (composed of filters 1211, 1212, 12110, 12111, 12113 and the subtracters 1213, 12112, 12114) and the second filter 122 (composed of filters 12210, 12211, 1229, 12213 and a subtracter 12212), the coefficient of the noise control filter 220 which optimally cancels the noise x_jto be controlled assumes the coefficient

[0450] Ã=[Ã(1)Ã(2) . . . Ã(I)]^T  Eq.(106)

[0451] which is left after the coefficient of the adaptive filter a(z) has converged.

[0452] (3-3) Control Flow From Power Activation:

[0453] The control procedure when the present invention is applied to the actual apparatuses will be described.

[0454] Firstly, just after the power activation, the coefficients of the feedback control filter 210 and the noise control filter 220 are not calculated yet. The coefficients of the both filters 210 and 220 are calculated only after the synthesized noise is transmitted from the loud speaker 203 and the closed circuit is formed.

[0455] However, if the coefficients are set, the closed circuit is formed, so that the danger of the howling occurrence immediately occurs. For this reason, it is necessary to carefully select the coefficients of the both filters 210 and 220 so as not to cause the howling.

[0456] Since the desired coefficients of the feedback control filter 210 have not been calculated yet upon the power activation,

[0457] {circumflex over (B)}=0  Eq.(107)

[0458] is one of the most appropriate coefficients. This coefficient does not increase the gain of the closed circuit more than the present state.

[0459] On the other hand, the coefficient of the noise control filter 220 has not been calculated yet. However, “A=0” can not be set for the coefficient of this filter. It is necessary that the secondary noise (white noise) is outputted from the loud speaker 203 for calculating the coefficient of the feedback control filter 210.

[0460] (3-11) Flow in Case of Providing Two Pairs of Coefficients to Noise Control Filter:

[0461] FIG. 28 shows a control flow. For a process upon the power activation, since it is necessary that an initial setting given by the above Eq.(107) is performed (at step ST1) and the coefficients A₁and A₂of the noise control filter 220 subsequently set form two independent equations, the relationship of

[0462] A₁^TA₂=0  Eq.(108)

[0463] is required to be satisfied.

[0464] For the coefficients to satisfy Eq.(108),

[0465] A₁=[a0 . . . 0]  Eq.(109)

[0466] A₂=[00 . . . a]  Eq.(110)

[0467] are selected (at steps ST2 and ST4) to provide, as a constant, such a small value as does not cause the howling.

[0468] The coefficients S₁and S₂of the non-recursive filter 271 (see FIG. 7) corresponding to the two coefficients A₁and A₂are sequentially calculated (at steps ST3 and ST5).

[0469] As the simultaneous equations have been obtained, from these A₁, A₂, S₁, and S₂, the difference D between the impulse response of the feedback path and the coefficient of the feedback control filter 210 is obtained by calculating “d” (at step ST6) for the coefficient of the adaptive filter 123 in the system identification circuit 120 of FIG. 24. The coefficient is added to the present coefficient {circumflex over (B)} of the feedback control filter 210 to provide

[0470] {tilde over (B)}={circumflex over (B)}+d  Eq.(111)

[0471] for updating the coefficient of the feedback path (at step ST7). With this {circumflex over (B)}, the coefficient  of the noise control filter 220 which is optimal to cancel the primary noise can be similarly calculated by using the system identification circuit 120 of FIG. 25 (at step ST8).

[0472] The important point is that  calculated at this time actually has an error in relation to an optimum coefficient A_opt. The error is highly independent, and there is left an independent component between the coefficient A₂previously set and the coefficient  newly obtained. If this independent component is utilized, it is possible to update the coefficient of the noise control filter 220 all the time by repeatedly applying the above coefficient update.

[0473] Namely, among the two coefficients previously set, if A₂is assumed to be A₁, S₂corresponding thereto is replaced with S₁(at steps ST9 and ST10), newly obtained coefficient A is assumed to be A₂to calculate S₂, again, and the same calculation is repeated, the coefficients of the noise control filter 220 and the feedback control filter 210 are updated all the time.

[0474] This also indicates that the coefficient of the feedback control filter 210 can be calculated by the arrangement that the coefficients of the noise control filter 220 and the feedback control filter 210 obtained during the last activation are preliminarily stored in the memory, and the stored coefficients are set in the both filters 210 and 220 upon the present power activation. If these stored coefficients are utilized, the effect of the active noise control can be obtained from the power activation in the system where the acoustic characteristic is relatively stable.

[0475] Thus, if the feedback control filter 210 simulates the feedback path well by the effect of the present invention, the ratio of the feedback component included in the output of the subtracter 211 used for the composition of the inverse filter decreases, and the calculation accuracy of the coefficient S of the non-recursive filter 271 deteriorates.

[0476] However, the deterioration only lowers the calculation accuracy 0 dB of the difference D. Even if the difference D can be obtained with the estimated accuracy 0 dB, it only means that the accuracy of the coefficient of the feedback control filter 210 is not improved. Namely, the present invention can be applied repeatedly.

[0477] (3-21) Flow in Case of Providing Two Pairs of Coefficients to Noise Control Filter:

[0478] FIG. 29 shows a control flow. Also in this case, upon the power activation the coefficients of the feedback control filter 210 and the noise control filter 220 have not been set yet. Therefore, the coefficient

[0479] Â=[a0 . . . 0]  Eq.(112)

[0480] is similarly set in the noise control filter 220 (at step ST11). Furthermore, for two pairs of independent coefficients set in the feedback control filter 210 for satisfying

[0481] {circumflex over (B)}₁^T{circumflex over (B)}₂=0  Eq.(113)

[0482] the following equations

[0483] {circumflex over (B)}₁=0  Eq.(114)

[0484] {circumflex over (B)}₂=[b0 . . . 0]  Eq.(115)

[0485] are provided (at steps ST12 and ST14).

[0486] The coefficients Â, {circumflex over (B)}₁, and {circumflex over (B)}₂are obtained with the coefficients of the non-recursive filter 261 being made S₁and S₂(at steps ST13 and ST15). The impulse response B of the feedback path is calculated as {tilde over (B)} by using the system identification circuit 120 shown in FIG. 26 (at step ST17).

[0487] {tilde over (B)} is newly provided for the coefficient of the feedback control filter 210, and the coefficient  of the noise control filter 220 which is optimal to cancel the primary noise is calculated by using the system identification circuit 120 of FIG. 27.

[0488] Since {tilde over (B)} has an error in relation to the optimum coefficient B_opt, it is possible to update the coefficient of the noise control filter 220 all the time by repeatedly applying thereto the above-mentioned coefficient update, with this error.

[0489] Namely, among the two coefficients previously set, if {circumflex over (B)}₂is assumed to be {circumflex over (B)}₁(at step ST19), S₁corresponding thereto is replaced with S₂(at step ST18), newly obtained coefficient {tilde over (B)} is assumed to be {circumflex over (B)}₂(at step ST20), S₂is calculated again, and the same calculation is repeated, the coefficients of the noise control filter 220 and the feedback control filter 210 are updated all the time.

[0490] The problem in this method is that by the coefficient update of the feedback control filter 210 the feedback component is well canceled, and the calculation accuracy of the coefficient {tilde over (B)} similarly deteriorates as the calculation accuracy of the coefficients S₂and S₁deteriorates. This deterioration disturbs the coefficient of the noise control filter 220, thereby causing the reduction of the noise canceling quantity.

[0491] The easiest method to solve this problem is that the coefficient update is stopped when the coefficient of the feedback control filter 210 obtains a sufficient accuracy. It can be determined by the fact that the update quantity of the coefficient of the feedback control filter 210 has become small.

[0492] Namely, when the difference R between {circumflex over (B)}₂and {tilde over (B)} decreases equal to or less than a fixed value R₀(at step ST16), the coefficient update of the feedback control filter 210 has only to be stopped. However, since there is a possibility that the generation process of the primary noise varies even that time, it is required to sequentially update the coefficient of the noise control filter 220 (at step ST21).

[0493] As described above, an active noise control apparatus of a feedback type according to the present invention [3] is arranged such that an inverse filter composing circuit forms a filter having a characteristic including a transfer function opposite to a closed circuit starting from the noise control filter and returning to the noise control filter again through both of the feedback path and the feedback control filter, a system identification circuit provides two pairs of different fixed coefficients either to the noise control filter or the feedback control filter to update a coefficient of an adaptive filter in order that a difference becomes a minimum between an output of a first filter forming a numerator of a solution obtained, from simultaneous equations based on two transfer functions of an inverse filter formed within the inverse filter composing circuit and an output of the adaptive filter connected to a second filter in cascade forming a denominator of the solution, and the system identification circuit is further repeatedly used for calculating the coefficient of the noise control filter optimally canceling the primary noise as the coefficient of the adaptive filter by making a numerator, which forms a ratio of the transfer function expressing the generation process of the primary noise obtained from the simultaneous equations and the transfer function of the feedback path previously identified on the system identification circuit, the first filter and making a denominator the second filter. Therefore, the coefficients of the feedback control filter and the noise control filter can be updated without outputting the white noise from the loud speaker during the active noise control.