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The Region of Convergence

February 2, 2019 by 3200 Creative

The Region of Convergence

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  1. Question 1 of 4
    1. Question

    The infinite series defining the z-transform converges for all possible values of z.

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  2. Question 2 of 4
    2. Question

    The z-transforms of two different time signals x[n] and y[n] can satisfy X(z) = Y(z).

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  3. Question 3 of 4
    3. Question

    It is possible to have a signal for which the z-transform does not exist for any values of z.

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  4. Question 4 of 4
    4. Question

    Identify all of the following that describe valid shapes for the region of convergence in the z-plane.

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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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