Digital filter design using weighted least squares techniques

This paper describes techniques for designing IRR digital filters with arbitrary log-magnitude specifications. The techniques use iterative weighted least squares (WLS) methods to arrive at filters that are nearly optimal when measured on a logarithmic magnitude scale. The error weighting function is updated at each iteration and can be chosen to provide results that approximate the ideal response in a least squares or a minimax sense. A novel weight updating strategy is proposed, that provides some computational advantages. It is shown that certain simplifying approximations are good when the approximation error is small