A numerical algorithm for complex Chebyshev FIR filter design
C.-Y. Tseng · 2003
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(>or=n+1) distinct frequency points and is solved iteratively using a new and efficient implementation of Lawson's algorithm which requires O((m-n)/sup 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(n/sup 2/) computations for each iteration of Lawson's algorithm where m-n is small compared to square root n.>