Design of digital all-pass filters using a weighted least squares approach

This paper considers the minimax design of digital all-pass filters via the FIR and IIR approximations. For the FIR digital all-pass filter design, the problem is appropriately formulated so that a recently-developed weighted least squares (WLS) algorithm can be used to efficiently solve the associated minimization problem. We also design FIR digital all-pass filters using the WLS algorithm to have equiripple group delay error. For the IIR digital all-pass filter design, we reformulate the design problem to result in a simple minimization problem. Therefore, a nonlinear minimax algorithm can be employed to obtain the solution. The key operation of the nonlinear minimax algorithm is to find the Chebyshev approximation of a desired function from a linear subspace. This can be efficiently solved by using the WLS algorithm. Several design examples demonstrating the effectiveness of the proposed approaches are also provided