Design of ARMA digital filters with arbitrary log magnitude function by WLS techniques

A technique is proposed for designing autoregressive-moving average (ARMA) digital filters to have an arbitrary log magnitude frequency response. The technique is based on an iterative weighted least-squares (WLS) approach in the frequency domain. A weight updating procedure is introduced to obtain a least-squares approximation to the given log magnitude function using the WLS approach. Filter coefficients are efficiently calculated using a fast recursive algorithm for a set of linear equations derived from the WLS problem. The technique is also extended to equiripple approximation with a minor modification of the weight updating procedure