Pole-zero decomposition: A new technique for design of digital filters

A new technique for design of digital filters is presented in this paper. The technique consists of splitting the given log magnitude response into two parts, one corresponding to the response of the numerator polynomial of the filter transfer function and the other part to the response of the denominator polynomial. The inverse of each of these polynomials is considered as an all-pole filter and the response of the all-pole filter is approximated by a small number of autoregressive coefficients. The autoregressive coefficients obtained for the numerator polynomial represent the zero part of the final filter and the coefficients obtained for the denominator polynomial represent the pole part of the final filter. With equal number of poles and zeros, the overall filter response can be made nearly equiripple in the passband and stopband. The amplitude of the ripple can be traded with the width of the transition band. The ripple characterstics can be controlled by appropriately choosing the number of poles and zeros of the filter.