A systematic technique for designing approximately linear phase recursive digital filters

A systematic design method is introduced for synthesizing approximately linear phase lowpass recursive 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 filter structures under consideration are the conventional cascade-form realization of the second- and first-order blocks and the parallel connection of two allpass filters (wave digital lattice filters). There are two different criteria for the transition band behavior of the filter. In the first case, it is required that in the transition band the maximum amplitude value be less than or equal to the passband maximum. In the second case, the amplitude response is required to be monotonously decreasing in the transition band. The overall synthesis technique consists of two basic steps. The first step involves finding in a simpler manner a good suboptimum filter. This filter is then used in the second step as an initial filter for further optimization. The optimization in the second step is performed by properly modifying the Dutta-Vidyasagar algorithms. 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 FIR equivalents especially in narrowband cases.