Magnitude and Delay Approximation of 1-D and 2-D Digital Filters

There are more than 100 books on Circuit Analysis, Network Synthesis, Ana- log and Digital Filters and Signal Processing written at the undergraduate and graduate level and a few more written as Reference and Handbooks. When and if they discuss the design of analog and digital filters, they treat mainly the approximation of the magnitude response of the filters and very little of their phase or group delay response. There is hardly any discussion of designing fil- ters that simultaneously approximate the magnitude and group delay response of the filters. Thus most of the books routinely discuss Butterworth, Chebyshev and sometimes the Cauer or elliptic function response of the lowpass prototype filters, followed by the transformations to design highpass, bandpass and band- stop filters-all of them approximating their magnitude response only. Due to the rapid progress from analog to digital communication and data transmission that has taken place in recent years, there is a greater need for designing filters that approximate both the magnitude and group delay requirements. So also is the need to design 2-dimensional digital filters, particularly those used in image processing, that approximate prescribed magnitude as well as constant group delay responses. A lot of research work has been published in professional jour- nals on the design of these filters in the last 10-15 years.