Filters Design by Z Transformation and Pascal Matrix

Adán Bonilla Chávez, Francisco García Ugalde, Bohumil Psenicka, and Jiri Hospodka


Bilinear transformation, Pascal matrix, Digital filters, Transer function


In the context of the digital filter design, a great deal of research has been done to facilitate their computation. The Pascal matrix defined in [1], [2] has provided its utility in this field. In this paper we summarize the direct transformation from low-pass continuous-time transfer function H(s) to discrete-time H(z) of the bandpass and bandstop transfer functions. This algorithm uses the Pascal matrix and is constructed from the rows of a Pascal triangle. The advantage of this method is that 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(s) if the discrete transfer function H(z) is known. Numerical example for matrices P, P1, Q and Q1 illustrate the practical utilization of this technique.

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