Design of approximately flat group delay selective IIR filters based on wave digital allpass filters

The wave digital allpass filter is a computationally efficient signal processing building block. In this thesis, we review the properties of allpass filters and consider the applications in digital filtering. The digital filter structures under consideration are the conventional cascade-form realization and the parallel connection of two allpass filters (wave digital lattice filters).; Given the attenuation specifications, the filter parameters as well as the slope of the linear phase response are optimized in such a way that the group delay is approximated flat in the passband. The problem of allpass filter design for group delay equalization is solved by using the nonlinear least squares method. On the other hand, the problem for group delay approximation can be solved by using pole-zero placement and a modified Remez algorithm, respectively.; The proposed design scheme for group delay equalization consists of two basic steps. The first step involves obtaining a filter with the desired attenuation based on pole-zero placement. An important feature of the proposed method is the possibility of placing the poles and zeros in their optimum positions. The method is also modified to design IIR filters with approximately flat group delay in the passband. In the second step, this filter is cascaded with an allpass compensation filter that is designed by the nonlinear least squares method. For IIR digital filters in the form of a parallel connection of two allpass subfilters, the modified Remez algorithm is applied. The rational approximation problem is transformed into a linear problem. The proposed algorithm converges after a few iterations, and the attenuation characteristic of the IIR digital filter is equiripple. Several examples are included illustrating the efficiency of the proposed methods.