Discretization of z-Plane Due to Quantization of Coefficients of IIR Allpass Filters

One of the important domains of digital signal processing is the development of IIR allpass digital filters that differ in phase response, and the magnitude response of which is constant at all frequencies. This paper is devoted to the extension of the new approach developed by the authors to the synthesis of IIR digital filters with a finite word length to allpass filters. This approach is based on the fact that the finite wordlength is taken into account even before structural synthesis at the stage of calculating zeros and poles. The calculated values of zeros and poles are final. The next stage of structural synthesis does not distort these values. At the stage of structural synthesis, structures are generated. In this paper, the topography of the poles and zeros of an allpass IIR digital filter with a finite word length is studied. These results are intended to be used at the first stage of the approach developed by the authors.