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

The authors propose a technique for designing IIR (infinite impulse response) 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 nearly optimal approximation to the given log magnitude function in the least-squares sense. The weighting function is updated using the results of the previous iteration in such a way that the weighted error approximates the log magnitude error. Filter coefficients at each iteration are efficiently computed using a fast recursive algorithm for a set of linear equations derived from the WLS problem. Several design examples demonstrate the rapid convergence of the design algorithm. The algorithm is extended to equiripple approximation by means of a minor modification of the weight updating procedure