The general biquadratic transformation of polynomials

An explicit formula for establishing the relationship between the original coefficients of a single-variable polynomial and the coefficients of the transformed polynomial, on application of the general biquadratic transformation, is derived. It is shown that all the hitherto known techniques for the bilinear transformation can be considered as special cases of the formula advanced here. Furthermore, the result was extended to a general Mth order polynomial transformation. The results obtained are pertinent to the design of digital filters from analog counterparts.<>