Abstract

A new z -domain continued fraction expansion ( CFE ) has been proposed. It is shown that the ratio of an anti-mirror-image polynomial to a mirror-image polynomial originating from the denominator of a transfer function can be expanded into this new type of z -domain CFE . Unlike the earlier types of z -domain continued fraction expansions, this new type is not unique for a given polynomial, and there will be a large number of possibilities. Algorithms have been proposed to obtain the various possible CFEs , which are implemented using MATLAB software. For the denominators of some well-known filters like Butterworth lowpass filters, Butterworth lowpass Complementary Pole-pair Filters (CPPF) and Chebyshev lowpass filters, the required coefficients of the CFEs are obtained. Also, starting from the coefficients of the CFEs , algorithms have been presented to generate stable transfer functions for filters such as lowpass, highpass and bandpass in the z -domain.