Theory and Procedure for Optimization of Low Pass Attenuation Characteristics

This paper is concerned with the problem of obtaining an insertion-loss function having a preassigned equal ripple in the pass band, and satisfying attenuation requirements with a maximum possible margin over the stop band. A major problem is involved in choosing attenuation poles so as to maximize the minimum of the difference between the attenuation function and the attenuation specification function. The existence and uniqueness of an optimal solution to this min-max problem are demonstrated in this paper. A simple optimality criterion is established as a necessary and sufficient condition, and this clarifies the nature of the problem. An iterative numerical procedure, suitable for digital computers, is supplied with proof of convergence. An illustrative example is also included.