An efficient implementation of Lawson's algorithm with application to complex Chebyshev FIR filter design

This paper presents an efficient implementation of Lawson's algorithm and illustrates its application in complex Chebyshev FIR filter design. It is shown that the update terms in Lawson's algorithm can be efficiently achieved by computing a proper subspace projection, provided that the number of points involved in Lawson's algorithm is sufficiently small (not much greater than n where n is the number of variables). An application of this particular implementation form for Lawson's algorithm is then demonstrated by using it to solve the subproblems involved in a multiple exchange algorithm. In particular, this exchange algorithm is based on generalizing Remez second exchange algorithm to the complex case which requires solving a sequence of subproblems where each subproblem is itself a complex Chebyshev approximation problem defined over a finite number of points; the subproblems are systematically defined using a simple exchange procedure. The effectiveness of this multiple exchange algorithm for designing complex FIR filters is illustrated through various design examples, including a long filter with length n=125.<
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