On the design of FIR filters by complex Chebyshev approximation

The long-standing problem of approximating a complex-valued desired function with a finite impulse-response (FIR) filter is considered. It is formulated as an equalization to be solved using complex-valued filters. The proposed algorithm deals directly with the complex error function, which depends linearly on the coefficients of the filter to be designed. The magnitude of this error function is minimized in the Chebshev sense using a generalization of the Remez exchange algorithm. The method can be used to design complex- or real-valued-selective systems as well. The well-known design of optimal FIR filters with linear phase is included here as a special case