An explicit formula for the general bilinear transformation of polynomials with its application (Q1101381)

An explicit formula for establishing the relationship between the original coefficients of a single-variable polynomial and the coefficients of the transformed polynomial upon application of the general bilinear transformation is derived. The derivation is based on an alternative approach which is simpler than existing schemes. The result is applied to produce efficient algorithms for the digital simulation of analog systems as well as for the realization of variable recursive digital filters.