Design of arbitrary complex coefficient FIR digital filters by complex weighted least squares approximation

Real weighted least squares (WLS) approach is extended to complex cases for designing arbitrary complex FIR filters. The method is based on an iterative complex WLS approach to obtain a least squares approximation to the desired complex frequency responses, and the weighting function at each iteration is updated using the result of the previous iteration, which leads to the optimal approximation in the complex Chebyshev sense. Some numerical design examples such as single-passband filters and complex all-pass filters are presented, which demonstrate the usefulness of the present approach