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

Note 46. Inverse z Transform via Partial Fraction Expansion:Case 1: All Poles Distinct with M < N in System Function

This note covers the form of the partial fraction expansion that can be used to compute the inverse z transform of system functions that have no repeated poles and in which the degree of the denominator polynomial exceeds the degree of the numerator polynomial. The method is based on the basic strategy discussed in Note 45. Alternative approaches for use on system functions that do not meet these constraints are covered in Notes 47 through 49.

The form of the partial fraction expansion discussed in this note is suitable for use on system functions of the form

46.1

where M < N, thus making H(z) a proper rational function.

The ...