When using the z-transform

Inside Collection (Course): Signals and Systems

Summary: This module describes the inverse Z-transform.

When using the z-transform

This "method" is to basically become familiar with the z-transform pair tables and then "reverse engineer".

When given

When dealing with linear time-invariant systems the z-transform is often of the form

If

Find the inverse z-transform of

Khan Lecture on Partial Fraction Expansion |
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When the z-transform is defined as a power series in the form

Now look at the z-transform of a finite-length sequence.

One of the advantages of the power series expansion method is that many functions encountered in engineering problems have their power series' tabulated. Thus functions such as log, sin, exponent, sinh, etc, can be easily inverted.

Suppose

Without going in to much detail

The Inverse Z-transform is very useful to know for the purposes of designing a filter, and there are many ways in which to calculate it, drawing from many disparate areas of mathematics. All nevertheless assist the user in reaching the desired time-domain signal that can then be synthesized in hardware(or software) for implementation in a real-world filter.

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Comments:"My introduction to signal processing course at Rice University."