Computer‐Aided Synthesis of Characteristic Polynomials

This chapter discusses the synthesis of the characteristic polynomials of lowpass lossless prototype filters using an efficient computer‐aided optimization technique. It specifies an unconstrained artificial function for the optimization process that includes the objective function, as well as the inequality and equality constraints. The chapter develops the appropriate objective functions for optimization to generate the known classes of filter functions. The technique described for the computer‐aided optimization of characteristic polynomials for minimum phase filters is equally applicable for linear phase filters, both symmetric and asymmetric. The efficiency of this procedure is demonstrated by including examples of the classical Chebyshev and elliptic function filters as special cases of the design procedure. The computed critical frequencies are specified in Appendix 4A. These data add to the range of unified design charts and also provide guidelines for developing software to synthesize characteristic polynomials for filters with arbitrary amplitude and phase response.