A systematic technique for designing approximately linear phase recursive digital filters

A systematic method is introduced for designing approximately linear phase low-pass recursive digital filters. The filter structures under consideration are the conventional cascade form realization and the parallel connection of two allpass filters (lattice wave digital filters). Given the amplitude specifications, the filter parameters as well as the slope of the linear phase response are optimized in such a way that the maximum phase deviation from this linear phase is minimized in the passband. The filters are designed such that either the maximum amplitude value in the transition hand is less than or equal to the passband maximum or the amplitude response is monotonically decreasing in this band. The design scheme consists of two basic steps. The first step involves finding, in a simpler manner, a good suboptimum filter. In the second step, this filter is then used as an initial filter for further optimization that is carried out by the second algorithm of Dutta and Vidyasagar. Several examples are included illustrating the efficiency of the proposed design scheme. They also show the superiority of the resulting recursive filters over their linear phase finite-impulse response equivalents, especially in narrow-band cases