Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 48. Inverse z Transform via Partial Fraction Expansion:Case 3: All Poles Distinct with M ≥ N in System Function (Implicit Approach)

This note presents a procedure for computing the inverse z transform for system functions in which all poles are distinct, and the degree, M, of the numerator equals or exceeds the degree, N, of the denominator. The approach presented herein is an alternative to the approach presented in Note 47.

In order for a rational function to be expanded as a sum of partial-fraction terms, the degree of the numerator must be less than the degree of the denominator. In cases where M ≥ N, the system function must be restructured as the sum of a polynomial, C(z), and a proper rational function, H_R(z):

48.1

where

This ...