The Mechanics of the Bilinear Transformation

The effect of the bilinear transformation substitution s 1 Z = -- s- on a polynomial equation nE aizi = 0 i= 0 is formulated in matrix terms. The matrices involved are formed by very simple rules. This procedure considerably facilitates calculation of the resulting s-polynomial, and makes the bilinear transformation an attractive tool for systems analysis rather than the textbook curiosity which it has been.