The bilinear Z transform by Pascal matrix and its application in the design of digital filters

Abstract

In this letter, the Pascal matrix is used for transforming the normalized analog transfer function H(s) from the lowpass to the lowpass and highpass discrete transfer functions H(z). This algorithm is very simple; therefore, the transfer function H(s) can be easily transformed to the z domain using an appropriate calculator. The inverse Pascal matrix can be obtained without computing the determinant of the system, and then it is very easy to obtain the associated analog transfer function H(s) if the discrete transfer function H(z) is known.