WLS design of complex FIR filters with prescribed phase error and magnitude error

Weighted least-squares design of complex FIR filters with given phase and magnitude errors is considered in this paper. We put constraints on the phase error and complex valued frequency-response error, and minimize the weighted sum of squared frequency-response error. The minimization problem is reformulated in a semi-definite programming (SDP) problem, and then solved with a well-developed interior-point method based SDP routine. By imposing a sigmoid upper bound on the phase error of the filter, we not only obtain prescribed phase error but also reduce the group-delay error.