Number theoretic fast algorithms for bilinear and other generalized transformations

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Abstract
Fast algorithms based on the Mersenne and Fermat number-theoretic transforms are used to perform the bilinear transformation of a continuous transfer function to a discrete equivalent. The computations are carried out in finite precision arithmetic, require no multiplications, and can be implemented in parallel using very simple processors. Although the bilinear transform is presently emphasized, similar algorithms are easily derived for any transformation from the s-plane to the z-plane involving the ratio of two polynomials with integer coefficients.