Z Transformation by Pascal Matrix and its Applications in the Design of IIR Filters

"In this work, we summarize a direct method to transform the low-pass continuous-time transfer function H(z) to several discrete-time H(z) transfer functions. Our algorithm uses the Pascal matrix that is built from the rows of a Pascal Triangle. The inverse transformation is obtained with the Pascal matrix without computing the determinant of the system, which simplifies the process to obtain the associated analog transfer function H(z) if the discrete transfer function H(z) is known. In addition, the algorithm is easy to program on a personal computer or scientific calculator because all the computations are made using matrices. The algorithm presented is illustrated with numerical examples."