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Definition of z-Transform

Definition of z-Transform

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.

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A z score (or standardized value) is measured in units of the standard deviation. It indicates how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a zero z score. It is important to note that the mean of the z scores is zero, and the standard deviation is one.
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Related Experiment Video

Updated: Aug 27, 2025

Using the optokinetic response to study visual function of zebrafish

Using the optokinetic response to study visual function of zebrafish

Published on: February 2, 2010

How do you Zoo?

Lauren Danridge¹, Bill Greer²

¹Animal Care & Use Office, University of Michigan, Ann Arbor, Michigan, USA. danridlm@umich.edu.

|September 23, 2022

Summary

No abstract available in PubMed .

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Last Updated: Aug 27, 2025

Using the optokinetic response to study visual function of zebrafish

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