Unified theory and state‐variable implementation of critical‐monotonic all‐pole filters

Abstract

SUMMARYThe subject of synthesis of critical-monotonic low-pass amplitude characteristics will be revisited. Several new contributions will be given in order to: facilitate the choice of the proper transfer function, to allow cataloguing the transfer functions, to simplify the circuit synthesis procedure, and to perform synthesis in the form of a statevariable continuous time active filter. Four main criteria for transfer function synthesis will be implemented: maximally flat at the origin, maximum slope at the band-edge, maximal asymptotic attenuation, and minimal amplitude distortion in the pass-band. For every criterion, a class of filters will be generated and the coefficients of the transfer functions will be calculated and published for the first time (with one exception). Properties of the classes so generated will be quantitatively compared for the first time. The state-variable structure will be advised as the one with the simplest synthesis procedure. The procedure will be explained and the design process will be exemplified. Statistical tolerance analysis will be performed for the example solutions in order to complete the information for comparison.

IIR digital filters with critical monotonic pass-band amplitude characteristic

“…Polynomial (or all-pole) filters with critical monotonic amplitude characteristics (CMAC) in the pass-band have been available for several decades now [1]. They are alternative to the two main non-monotonic classes of polynomial filters: the Chebyshev (C), often referred to as equiripple pass-band filters and the least-squares (LS) being a subclass of the so called least-pth approximation [2].…”

“…There are four main classes of CMAC as discussed in [1,5]. They originate from the design criteria implemented for synthesis of the transfer function.…”

“…A catalog of the coefficients of the transfer functions of all four classes of CMAC for n up to 10, obtained by these criteria, was published in [1] where a comparative study is given too.…”

“…Unfortunately, as shown in [1] and elsewhere, practically all classes of CMAC functions outperform the Butterworth solution in all respects. So, a decision was taken to develop a procedure for digital filter design exhibiting CMAC properties.…”

“…The critical monotonic amplitude characteristic (CMAC) for allpole (polynomial) transfer functions was introduced almost half a century ago as discussed in [1]. CMAC filters represent an extension to the broad family of filtering functions having all transmission zeroes at infinity.…”