A numerical algorithm for complex Chebyshev FIR filter design

The author presents a multiple exchange algorithm which solves the complex Chebyshev approximation problem by systematically solving a sequence of subproblems. Each subproblem involves optimization over m(⩾n+1) distinct frequency points and is solved iteratively using a new and efficient implementation of Lawson´s algorithm which requires O((m-n)² m) computations per iteration, where n is the filter length. In general, by carefully selecting the frequency points in each subproblem, it is possible to control m so that m-n always remains small. The new algorithm also guarantees global optimum convergence and requires less than O( n²) computations for each iteration of Lawson´s algorithm where m-n is small compared to √n