Optimal design of FIR filters with the complex Chebyshev error criteria

Abstract

We present an improved algorithm for an established filter design problem, the design of an FIR filter that best approximates, in the complex Chebyshev sense, a desired complex-valued frequency response. The algorithm is a variant of the simplex algorithm of linear programming, which has an interpretation as an implicit multiple exchange. It is iterative, robust, and exhibits good convergence speed. Global optimum convergence is guaranteed. Both complex and real-valued impulse responses can be designed with it; the design of complex coefficient filters is new. An example is given for each case. The design of noncausal filters is new. In addition to these new applications, we conjecture that this new algorithm may have important advantages over existing techniques, with respect to the maximum filter length possible, speed and stability of convergence, accuracy, and memory requirements. The ability to design long filters is among the more significant improvements over previous work. Filters of length 1000 have been designed with the new method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>