A unified approach to multistage frequency-response masking filter design using the WLS technique

This paper presents a unified approach to the optimal design of sharp linear-phase finite-impulse-response (FIR) digital filters synthesized using the multistage frequency-response masking (FRM) technique. In this approach, the design of a k-stage FRM filter is achieved in a recursive manner. The minimax design problem arising at each step of the synthesis process is converted into a corresponding weighted least-squares (WLS) problem. The WLS problem is highly nonlinear with respect to the coefficients of the filter. Consequently, it is decomposed into several linear least-squares (LS) problems, each of which can be solved analytically. It is then solved iteratively by using an alternating variable approach. Numerical design examples are included to demonstrate the effectiveness of the method.