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Properties of the Region of Convergence

February 2, 2019 by 3200 Creative

Properties of the Region of Convergence

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Question 1 of 4

1. Question
Poles of a z-transform can lie inside the region of convergence
- True
- False
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Question 2 of 4

2. Question
The z-transform $X(z)$ converges on the unit circle, $|z| = 1$ . Select all of the statements that apply.
- The absolute values of the signal $|x[n]|, n = \ldots, -2, -1, 0, 1, 2, \ldots$ sum to a finite number
- The z-transform has no poles inside of $|z| = 1$
- The DTFT of the signal exists
- The z-transform has no poles outside of $|z| = 1$
- The z-transform has no zeros on the unit circle, $|z| = 1$
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Question 3 of 4

3. Question
The region of convergence for $X(z)$ is the ring $0.5 < |z| < 3$ . Select all of the statements that apply.
- All the poles of $X(z)$ lie within the ring $0.5 < |z| < 3$
- The signal is left sided
- The signal is right sided
- The signal is two sided
- The DTFT of the signal exists
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Question 4 of 4

4. Question
The ROC of a z-transform lies outside of a circle of radius 2 in the z-plane. Select all of the statements that apply.
- The signal is finite duration
- The signal is left sided
- The signal is right sided
- The signal is two sided
- All the poles are inside a circle of radius 2
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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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