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Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation by C. Britton Rorabaugh

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Note 44. The z Transform

The z transform is a mathematical tool that plays a role in the analysis of discrete-time systems similar to the role played by the Laplace transform in the analysis of lumped-parameter continuous-time systems. It has a place in the theoretical exploration of all linear shift-invariant discrete-time systems, but in practice, the z transform (and its relationship to the Laplace transform) is most commonly used in the design of IIR filters. In fact, some authors, such as Lyons [1], discuss the z transform only in conjunction with IIR filter design.

Sometimes, pole and zero locations (which are features obtained from the z transform) are used as visualization aids to provide insight into the behavior of adaptive filters ...

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