Implementation considerations and comparisons of Chebyshev approximation algorithms for complex functions

The problem of delay equalization in the design of SAW transducer weighting functions is considered. The need arises for an approach to the synthesis of finite impulse response functions with an arbitrary complex frequency response. Of late, several algorithms have been presented. The approach investigated is an adaptation of this previous work of the design of FIR functions by Chebyshev approximation using a complex error function. This error function is minimized in the Chebyshev sense using a generalization of the Remez exchange algorithm, which is an iterative approach, for simultaneous solution of both the magnitude and phase responses. The algorithms´ convergence characteristics are considered with respect to the application to the design of SAW transducers with a large FIR filter order. The goal is to optimize the algorithm and its convergence for near real-time performance on desktop computing environments. The algorithms´ differences are presented with examples and performance values