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

Note 45. Computing the Inverse z Transform Using the Partial Fraction Expansion

Often IIR filters are designed in the z domain, and in order to obtain the filter’s unit sample response, it is necessary to compute the inverse z transform of the filter’s system function. This note provides an overview of the partial fraction expansion (PFE) technique that can be used to compute the inverse z transform. Notes 46 through 48 cover the specifics of how the PFE is applied to system functions exhibiting various properties, as detailed in the “Related Notes” sidebar on the next page.

There are a handful of fundamentally different approaches for inverting the z transform, and each of these approaches can have several different minor variations. Most of ...