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Poles and Zeros of the z-Transform

February 8, 2019 by 3200 Creative

In this lesson you will learn how to find the poles and zeros of a rational z-transform. Poles and zeros are important because they provide a very insightful characterization of systems described by linear constant coefficient difference equations. Such systems are widely used to implement filters and as mathematical models for signals. The poles and zeros indicate the stability and causality properties of a system as well as give insight into the frequency and impulse response, topics studied in subsequent lessons.

Prerequisites

  • The Region of Convergence for the z-transform

Key Concepts and Screenshots

Concepts and Screenshots for Poles and Zeros

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1

Poles and Zeros


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Course Lessons

  • Introduction to the [latex]z[/latex]-Transform

  • The Region of Convergence for the [latex]z[/latex]-Transform

  • Poles and Zeros of the [latex]z[/latex]-Transform

  • Properties of the Region of Convergence

  • Inversion of the [latex]z[/latex]-Transform via Power Series Expansion

  • Inversion of the [latex]z[/latex]-Transform: Partial Fraction Expansion

  • Properties of the [latex]z[/latex]-Transform

  • [latex]z[/latex]-Transform Analysis of LTI Systems

  • Stability and Causality of LTI Systems Described by Difference Equations

  • Inverse Systems for LTI Systems Described by Difference Equations

  • Minimum-Phase and All-Pass Systems

  • Frequency Response Magnitude and Poles and Zeros

  • Impulse Response and Poles and Zeros

Courses

  • Foundations

  • Time Domain LTI Systems

  • Fourier Series and Transforms

  • Sampling and Reconstruction

  • The DFT and Applications

  • The Z-Transform

  • Intro to Filter Design

  • IIR Filter Design

  • 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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