Arbitrary polynomial transformations

Previously, we looked at several polynomial transformations-the classical lowpass-to-highpass, lowpass-to-bandpass, and lowpass-to-bandstop transformations, and the special case of the bilinear transformation. We presented specific algorithms for accomplishing the transformations numerically. In this article, we end our preoccupation with polynomial transformations by presenting a straightforward algorithm derived from Heinen and Siddique [1988] for performing arbitrary polynomial transformations numerically, and, which is, in fact, based on Waggener's method [1980]. However, we do not implement Heinen and Siddique's algorithm directly. Instead, we rely on functions written to find sum-polynomials and product-polynomials. Our approach is quite as efficient, but it should prove easier to follow and code.