Design of high-order Chebyshev FIR filters in the complex domain under magnitude constraints

This article discusses the design of FIR filters that approximate a complex-valued target frequency response in a Chebyshev sense. Additionally, the required stopband attenuation can be specified. Solving the dual of a semi-infinite linear program is currently the most efficient way to design such filters, but numerical problems prevent the design of high-order FIR filters. Modifications are proposed to overcome this limitation. Furthermore, an efficient method is presented for generating starting values that are close to the optimal solution such that the number of iterations is considerably reduced. Examples of filters with a length up to 250 taps are included.