Synthesis of spectrum shaping digital filters of recursive design

Several techniques are presented, both iterative and noniterative, for synthesizing a´ recursive digital filter whose amplitude spectrum approximates a desired shape. The synthesis is carried out by implementing known algorithms for rational function approximation of a continuous function on a finite interval. In particular, techniques for synthesizing the best rational function approximation in the Chebyshev sense and in the least squares sense are treated. Examples are given which illustrate the quality of approximation achievable through each technique.