Anti-aliasing filter with automatic cutoff frequency adaptation

[0002] The present invention generally relates to low-pass filtering of electrical signals, and more particularly to a low-pass filter having an adjustable cut-off frequency.

[0003] When an analog signal is sampled, spectral components at frequencies greater than one half the sample rate are overlaid on the components below one half the sample rate. This effect, known as aliasing, can sometimes be exploited as a benefit. However, aliasing is mostly considered detrimental and results in a noisy signal.

[0004] Aliasing is typically addressed by interposing a low-pass anti-aliasing filter before the analog-to-digital converter (ADC). If the maximum frequency of interest is f_maxand the sample rate is f_s, the anti-aliasing filter must have a pass band from DC to f_max, a transition band from f_maxto (f_s−f_max), and a stop band above (f_s−f_max).

[0005] Conventional integrated-circuit analog filter design techniques involve building into silicon the components (resistors, capacitors etc.) that define the frequency characteristics of the filter. Thus, once a chip is made, the frequency characteristics of the filter are fixed. This approach limits the range of applications for which a particular device is suitable. For example, if a filter and an ADC are integrated with a field programmable gate array (FPGA) in a device, the pass band, transition band, and stop band are fixed at the time the device is made. However, users will likely desire different frequency bands for different applications. Since all the desired frequency bands are generally unknown at the time the device is made, the device will be suitable for only certain applications.

[0006] A circuit arrangement that address the aforementioned problems, as well as other related problems, is therefore desirable.

[0007] An anti-aliasing filter with adaptable cutoff frequency is provided in various embodiments of the invention. In one embodiment, the filter includes a calibrator/adaptor section and an anti-aliasing filter section. Both sections include a cascaded arrangement of adjustable delay circuits, and the calibrator/adaptor section includes a control circuit. A reference signal is input to the delay circuits and the control circuit of the calibrator/adaptor section, and an analog input signal is input to the delay circuits of the anti-aliasing filter. The control circuit compares the directly received reference signal to the reference signal from the last delay circuit and generates an adjustment signal responsive to the comparison. The delay intervals of all the delay circuits are adjustable responsive to the adjustment signal from the control circuit. In another embodiment, the anti-aliasing filter is used in an analog-to-digital conversion (ADC) system having a selectable sample clock rate. When the base sample clock rate is a lower frequency, the input analog signal bypasses the anti-aliasing filter and is input to an ADC circuit, which over-samples and digitizes the signal responsive to a multiplied base sample clock rate. The digital data is then decimated for compliance with the base sample rate. When the base sample clock rate has a higher frequency, the input analog signal is input first to the anti-aliasing filter and then to the ADC circuit. The ADC circuit does not over-sample when operating at the higher frequency, and therefore, no decimation of the data is required.

[0008] In another embodiment, the anti-aliasing filter is used in a digital-to-analog conversion (DAC) system having a selectable sample clock rate. When the base sample rate of the system is a lower frequency, digital data are interpolated responsive to a multiplied base sample rate. The interpolated data is thereafter converted to an analog signal by a DAC circuit. When the base sample rate is a higher frequency, the digital input is converted to an analog signal, bypassing the interpolation. The anti-aliasing filter is used to implement a reconstruction filter, which filters the analog signal from the DAC circuit.

[0009] Various other embodiments are set forth in the Detailed Description and Claims which follow.

[0010] Various aspects and advantages of the invention will become apparent upon review of the following detailed description and upon reference to the drawings in which:

[0011] FIG. 1 illustrates a device having an analog ADC/DAC arrangement and programmable circuitry in accordance with one embodiment of the present invention;

[0012] FIG. 2 is a schematic of a filter arrangement having an adaptable cut-off frequency in accordance with one embodiment of the invention;

[0013] FIG. 3 is a functional block diagram of an ADC system having a digital decimation filter in combination with an adaptive anti-aliasing filter;

[0014] FIG. 4 is a functional block diagram of a reconstruction system in accordance with one embodiment of the invention; and

[0015] FIG. 5 is a functional block diagram of a reconstruction system having a digital interpolation filter in combination with an adaptive anti-aliasing filter.

[0016] Various embodiments of the present invention are described in terms of analog-to-digital converter (ADC) and digital-to-analog converter (DAC) arrangements. It will be appreciated, however, that the invention is not so limited. Also, those skilled in the art will appreciate that the invention could be adapted to suit the requirements of other filter arrangements implemented in other types of programmable logic devices (PLDS) or ASICs.

[0017] FIG. 1 illustrates a device 52 having an analog ADC/DAC arrangement and programmable circuitry in accordance with one embodiment of the present invention. The programmable circuitry includes for example, circuitry used in PLDs. Example PLDs include FPGAS, CPLDS, and PLAS. PLDs are becoming popular in applications such as digital signal processing (DSP), and the advantages of PLDs include programmability in combination with circuit-like speeds.

[0018] Conventional DSP arrangements may include various analog circuitry for filtering and conversion between the analog and digital domains in combination with PLDs programmed to process the digital data. Device 52 is a chip that has both analog ADC/DAC circuit arrangements and circuits comprising a conventional PLD. ADC/DAC arrangement 54 comprises circuitry for processing analog signals, and circuitry 56 is programmable for processing digital signals. Combining the analog circuitry with the PLD eliminates the need for separate analog devices and eliminates inefficiencies of low levels of integration. The combined circuitry also eliminates the additional printed circuit board area required for multiple devices.

[0019] ADC/DAC arrangement 54 includes various filters, an ADC component, and a DAC component. The ADC receives an analog input signal on line 58, converts the analog signal to digital data, and provides data to circuitry 56 via an input port (not shown). The DAC receives digital data from circuitry 56 via an output port (not shown) and converts the data to an analog signal, which is output on line 60. It will be appreciated that in other embodiments, device 52 could be arranged with only one of the ADC or DAC, depending on specific application requirements.

[0020] Circuitry 56 includes programmable resources of device 52. For example, the programmable logic, programmable digital I/O resources, and programmable routing circuitry of a PLD comprise circuitry 56.

[0021] A basic anti-aliasing technique is to restrict the maximum frequency of the sampled signal to half the sample rate. Since it is impracticable to build an almost ideal low-pass filter with a sharp cut-off between frequencies that are to be passed and those that are to be rejected, filters are sometimes built such that the sampling rate is some multiple (greater than 2) of the cut-off frequency.

[0022] To integrate various filter circuitry with PLD circuitry presents various challenges as described above. For example, different applications will have different sample rates and therefore, different filtering requirements. Since it would be desirable to make device 52 appealing to a wide range of users, it would be desirable to make the analog filter characteristics of the ADC/DAC arrangement adjustable.

[0023] FIG. 2 is a schematic of a filter arrangement having an adaptable cut-off frequency in accordance with one embodiment of the invention. The example adaptive anti-aliasing filter arrangement 90 has two main components: anti-aliasing filter 102 and calibrator/adapter arrangement 104. In one embodiment, filter 102 is an analog implementation of a Finite Impulse Response (FIR) filter, and calibrator/adapter 104 calibrates and adapts the cut-off frequency of the circuit arrangement based on the period of an input reference signal. Other filter structures such as Infinite Impulse Response (IIR) filters could be used in place of FIR filter 102.

[0024] Blocks 106-1 through 106-(N−1) are analog delay lines connected in a cascade arrangement. The delays are adjustable as indicated, for example, by line 103, which is driven by control circuit 112. The outputs of blocks 106-1 through 106-(N−1) are sometimes referred to as “taps”. The taps provide access to discrete points in a time history of the signal. The delayed signals are weighted and summed in operational amplifier 108.

[0025] The weight of each tap is set by the ratio of the associated resistor to the feedback resistor R_F. For example, the weight at the tap of block 106-3 is the ratio of R₃to R_F. Thus, the shape of the filter characteristic depends more on the relative accuracy of the resistors than the absolute accuracy. The weights of the taps define the shape of the filter characteristic, and may be selected using known filter synthesis programs.

[0026] Whereas, the basic shape of the filter characteristic is defined by the resistors, the absolute value of the cut-off frequency depends on tau, which is the absolute delay of each individual block. More specifically, the cut-off frequency varies in inverse proportion to tau. Since each delay is adjustable (as controlled by control circuit 112 which is responsive to an input reference signal), the cut-off frequency is also adjustable.

[0027] Calibrator/adapter 104 is a DLL-like (delay-locked loop) arrangement that includes a cascaded arrangement of taps. A signal having a known period is passed through taps 110-1 through 110-(M−1), and the total delay through the taps is adjustable to one period of the input signal. Control circuit 112 compares the delayed signal with the input signal and continuously adjusts taps 110-1-110-4 such that the total delay is exactly one period of the input signal. Control element 112 can be implemented using known phase comparator arrangements.

[0028] Taps 106-1-106-(N−1) of filter 102 are constructed to match taps 110-1-110-(M−1) in calibrator 104. Thus, the delays and the corresponding cut-off frequency are accurately defined by the input signal. Each of taps 106-1-106(N−1) and 110-1-110-(M−1) can be built with a network operational amplifiers having known delays. The delay of each of the taps can be controlled by selecting which of the amplifiers are used. Alternatively, each of the delay elements could be implemented with a network of transistors having delays that are controllable by the applied voltage level. Other known implementations could also be used for the taps.

[0029] If each tap is implemented such that the associated delay can be varied over a relatively wide range, the input reference signal can be used not only to guarantee the accuracy of the cut-off frequency, but also to control the actual cut-off frequency. Since the cut-off frequency varies in inverse proportion to tau and tau is inversely proportional to the frequency of the reference signal, the cut-off frequency varies in proportion to the frequency of the reference signal. In one embodiment, the sample clock used to drive ADC 116 is used to adapt the cut-off frequency of filter 102.

[0030] Note that both the analog input and the analog output signals are continuous-time signals, as opposed to discrete time analog sampled signals.

[0031] While filter 90 is a continuous-time analog circuit, it displays some characteristics of a digital filter. Because the filter is implemented using non-zero separation between the taps, alias frequencies will be created as if it had a digital sample rate equal to the inverse of tau. Thus tau must be made small enough, and consequently, the effective sample rate high enough that a trivial pre-filter is all that is needed. Filter 90 has the advantage that its effective sample rate can be much higher than an equivalent computationally limited digital filter.

[0032] The number of taps, M, in the calibrator/adaptor 102 determines the relationship between tau and the sample rate. The number of taps in the filter, N, is determined by the desired filter characteristic.

[0033] For example, if f_sis three times f_max, the anti-aliasing filter must reject all components above 2f_max(=f_s−f_max). Achieving this rejection without the invention would require an external filter with a non-trivial rate of roll-off. Instead, the anti-aliasing filter of the invention together with a simple external filter provides the necessary rejection. If M is chosen to be 4, the effective sample rate is 12f_max, and the external pre-filter has from f_maxto 11f_maxto roll off. This filter would be much simpler.

[0034] A desirable characteristic in an anti-aliasing filter is linear phase response. That is, the filter acts like a delay, creating no relative differences in phase between frequency components. The filter affects the relative amplitudes of the frequency components and is achieved by making the weights symmetrical about the center of the delay lines (R₁=R_N, R₂=R_N−1, . . . ).

[0035] FIG. 3 is a functional block diagram of an ADC system having a digital decimation filter in combination with an adaptive anti-aliasing filter. In one embodiment, anti-aliasing filter 156 can be implemented as anti-aliasing filter 90 (described above). The cost of implementing this adaptive anti-aliasing filter increases as the minimum cut-off frequency it can support decreases. This increase is caused by the larger delay lines needed to provide longer delays for lower cut-off frequencies. Economic considerations dictate the minimum frequency at which the anti-aliasing filter 156 can operate.

[0036] At frequencies low enough for the ADC to operate at a multiple of the desired sampling rate, an alternative approach is available that may be more cost effective. The data is initially over-sampled, and the sample rate is then reduced to that desired using a digital decimation filter. The over-sample rate is equivalent to the effective sample rate in the analog filter and permits the use of a pre-filter (not shown) for anti-aliasing. The digital decimation filter provides the same filter characteristic as the analog anti-aliasing filter. After filtering, the sample rate may be reduced by simply discarding samples. It will be appreciated, however, that such a system is impracticable at high frequencies since the ADC may not be able to handle the over-sampling rate.

[0037] The analog anti-aliasing filter 156 has a minimum cut-off frequency sufficiently low for the over-sampling approach to support any demands for a lower cut-off frequency.

[0038] A sample clock input signal is input on line 150 to clock multiplier 152 and selector 154. At lower frequencies, clock multiplier 152 multiplies the sample clock signal to give a higher sample rate. The higher sample rate allows over-sampling of the input. At higher frequencies the sample clock signal on line 150 is selected, and at lower frequencies, selector 154 selects the output from clock multiplier 152.

[0039] The analog input signal is input to both anti-aliasing filter 156 and to selector 158. At higher frequencies, selector 158 provides the output of the anti-aliasing filter to ADC 160 for sampling at the rate of the sample clock. At lower frequencies, the selector provides the input analog signal directly to the ADC where it is over-sampled (in response to the multiplied sample clock signal).

[0040] The output signal from selector 158 is input to ADC 160, which can be implemented using conventional circuitry. The digital output from ADC 160 is input to both digital decimation filter 162 and to selector 164. At higher frequencies the output signal from ADC 160 is selected, and at lower frequencies (where the sample clock was multiplied), selector 164 selects the output signal from decimation filter 162. Decimation filter 162 low-pass filters the signal and selectively discards samples. For example, if the clock rate is multiplied by 4, then decimation filter may remove every second, third, and fourth sample, thereby restoring the stream of digital samples to the original sample clock rate.

[0041] In one embodiment, selectors 154,158, and 164 are controlled by a single configuration bit stored in the PLD. This bit allows the user to choose at design time which path is appropriate for the application. When the bit is set to support a high sample clock frequency, selectors 154, 158, and 164 implement the paths indicated by solid lines. When the bit supports a low sample clock frequency, paths indicated by the dashed lines are implemented.

[0042] In other embodiments, control of selectors 154, 158, and 164 allows additional options. For example, selectors 158 and 164 may be controlled to select both of analog anti-aliasing filter 156 and digital decimation filter 162 regardless of whether selector 154 selects clock multiplier 152.

[0043] FIG. 4 is a functional block diagram of a reconstruction system in accordance with one embodiment of the invention. It will be appreciated that the filter characteristic required to reconstruct an analog signal from a set of samples is identical to the filter used for anti-aliasing. Thus, the same adaptive anti-aliasing filter arrangement described in conjunction with FIG. 2 can also be used as a reconstruction filter.

[0044] The sample rate used to reconstruct an analog signal from the digital data is controlled by a sample clock signal that is input on line 202. The digital data from which the analog signal is generated is input to register 204, which is clocked by the sample clock. DAC 206 reads data values from register 204 and converts the data into an analog signal that is fed into adaptive low-pass filter arrangement 208. Filter arrangement 208, which is implemented in accordance with the teachings of FIG. 2, removes undesirable components from the analog signal and is adaptable to a range of sample rates. As in the input case, a trivial analog post filter may be required.

[0045] Analogous to the above described techniques for extending an ADC system to operate at lower sample rates using over-sampling, the DAC system can also be adapted to operate at lower sample rates.

[0046] FIG. 5 is a functional block diagram of a DAC system having a digital interpolation filter in combination with an adaptive reconstruction filter. As described in conjunction with the anti-aliasing example, it is uneconomic to use the adaptive filter at low frequencies. However, a digital interpolation provides an equivalent benefit to that of the digital decimation filter. The sample rate provided to the DAC is increased by adding additional samples between the existing samples. Consequently, only a trivial external reconstruction filter is required.

[0047] A sample clock input signal is input on line 150 to clock multiplier 152 and selector 154. At lower frequencies, clock multiplier 152 multiplies the sample clock signal to give a higher speed clock. The interpolation filter provides samples that match this faster clock. At lower sample clock frequencies, selector 154 selects the output from clock multiplier 152, and at higher sample clock frequencies the sample clock signal on line 150 is selected.

[0048] Digital data are input to both digital interpolation filter 256 and selector 258. The output signal from selector 258 is input to DAC 260, which can be implemented using conventional circuitry. The digital output from DAC 260 is input to both analog reconstruction filter 262 and to selector 264. At lower sample clock frequencies (where the sample clock is multiplied), selector 258 selects the output signal from interpolation filter 256, and at higher frequencies the directly input digital data is selected. Interpolation filter 256 selectively interpolates data values. For example, if the clock rate is multiplied by 4, then interpolation filter 256 may interpolate second, third, and fourth data values for each input value in order to provide digital data values equal in number to the multiplied sample clock rate.

[0049] The data selected by selector 258 are input to DAC 260, which converts the digital data to an analog signal. It will be appreciated that DAC 260 includes buffers (not shown) that are suitable for storing the digital data.

[0050] The analog signal is input to both reconstruction filter 262 and to selector 264. At lower sample clock frequencies, the direct path is selected, and at higher sample clock frequencies the data from the analog reconstruction filter is selected. In both cases, a trivial post filter may be required.

[0051] As in the anti-aliasing filter, a single configuration bit set by the user at design time may control selectors 154, 258, and 264 to route data through the appropriate path. Alternatively, more than one bit may control selectors 154, 258, and 264 so that more modes of operation are available. For example, both of interpolation filter 256 and analog reconstruction filter 262 may be used at the same time.

[0052] The present invention is believed to be suitable for a variety of device types and has been found to be particularly suited for implementation on an FPGA. Other aspects and embodiments of the present invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. For example, while the above description refers to low pass anti-aliasing filters, the invention can also be used with band pass anti-aliasing filters having both low and high cut-off frequencies. In other applications, the filter of the invention can be used as a low pass filter, band pass filter, or a high pass filter. It is intended that the specification and illustrated embodiments be considered as examples only, with a true scope and spirit of the invention being indicated by the following claims.