## 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 ...