Simultaneous amplitude and phase approximation for lumped and sampled filters

Abstract

SUMMARYA simultaneous amplitude and phase approximation method is presented for reciprocal and non-reciprocal lumped or sampled filters realized by LC, CCD, active RC, cascaded SC, digital or wave digital IIR filters. The approximation is based on the fictive decomposition of a non-minimum phase filter into a minimum phase and an allpass network in such a way that some poles and zeros should coincide with each other and so the filter order should decrease. In this way the amplitude and phase approximations can be carried out alternately, though the minimum phase and the allpass networks do not occur in the resulting filter. Both approximations are based on linear interpolation of specified functions with a possible application of the Remez algorithm. The interpolation algorithms can be used in other arbitrary approximation problems as well. Illustrative examples are given for some lowpass and bandpass filters.

A Systematic Algorithm for the Synthesis of Multiplierless Lattice Wave Digital Filters

“…The main drawback in this approach is that the phase response of the frequency-selective filter is usually very nonlinear and, therefore, a very high-order phase equalizer is needed in order to make the phase response of the overall filter approximately linear. It has turned out (Földvári-Orosz et al, 1991;Jaworski & Saramäki, 1994;Jones et al, 1991;Lawson & Wicks, 1992;Leeb, 1991;Surma-aho, 1997;Surma-aho & Saramäki, 1999) to be more beneficial to implement an approximately linear-phase recursive filter directly without using a separate phase equalizer. In the design techniques described in (Földvári-Orosz et al, 1991;Jaworski & Saramäki, 1994;Jones et al, 1991;Lawson & Wicks, 1992;Leeb, 1991;Surmaaho, 1997;Surma-aho & Saramäki, 1999), it has been observed that in order to simultaneously achieve a selective magnitude response and an approximately linear-phase performance in the passband, it is required that some zeros of the filter be located outside the unit circle.…”