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Properties of the z-Transform

August 10, 2019 by

The z-transform has several important properties. In this lesson you will learn the most commonly used properties of the z-transform in the analysis of signals and systems. In particular, the convolution-multiplication property introduces the characterization of linear time-invariant systems using the z-transform of the impulse response, which is called the system function. The time-shift property allows us to easily find the system function for a system described by a linear constant coefficient difference equation. The system function is the basis for using z-transforms to study systems, the topic of the following six lessons.

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  • Foundations

  • Time Domain LTI Systems

  • Fourier Series and Transforms

  • Sampling and Reconstruction

  • The DFT and Applications

  • The Z-Transform

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  • FIR Filter Design

  • Random Signal Characterization

  • Basis Representations of Signals

  • Estimation of Power Spectra and Coherence

  • Introduction to Signal Estimation and Detection Theory

  • MMSE Filtering and Least-Squares Problems

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