Design of FIR filters by complex Chebyshev approximation

The authors present an algorithm for designing an optimal FIR (finite impulse response) filter with real coefficients that best approximates an arbitrary complex-valued frequency response. This algorithm is theoretically guaranteed to converge with each iteration requiring O(N²) computations, where N represents the filter length. The properties of the optimal filter are derived and presented, and particular attention is paid to the case where the desired filter has arbitrary constant group delay