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