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

摘要

The 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 state-variable 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.