Design of arbitrary FIR log filters by weighted least squares technique

An efficient method to design FIR filters with arbitrary log magnitude and phase responses is proposed. The method is based on an iterative weighted least squares (WLS) approach to obtain a nearly optimal approximation to the given log magnitude function in the least squares sense. The weighting function at each iteration is updated using the result of the previous iteration, which leads to an equiripple approximation in the log magnitude error. The method can be easily modified to approximate arbitrary log complex-valued frequency response, such as complex FIR log filters. Several examples are illustrated to show the effectiveness of the present approach