Signals & Systems

Signal Classification

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LTI Systems

System Classification Linearity Test Time Invariance Test Impulse Response Convolution Integral Convolution Properties Convolution Sum Step Response Causality from Impulse Response BIBO Stability Cascade and Parallel Systems Feedback Systems Invertibility

Fourier Series

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Fourier Transform

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Laplace Transform

Laplace Transform Definition Region of Convergence LT of Standard Signals Laplace Transform Properties Initial Value Theorem Final Value Theorem Inverse Laplace Transform Inverse LT of Repeated Poles Transfer Function Pole Zero Plot Laplace System Analysis Using Laplace

Z-Transform

Z-Transform Definition Z-Transform ROC Z-Transform of Standard Sequences Z-Transform Properties Inverse Z-Transform Transfer Function H(z)Stability from Z-Transform

Sampling & Reconstruction

Sampling Theorem Aliasing Ideal Reconstruction Practical Reconstruction Anti-Aliasing Filter Sampling of Discrete Time Signals

Z-Transform ROC

ROC shapes, causal and anti-causal, stability criteria.

Darshan N

Updated: 19 March 2026

10 min read

#Signals & Systems

Z-Transform ROC

Test your understanding of region of convergence shapes and stability criteria for Z-transforms.

Question 1 of 3

Q1.A causal LTI system has a Z-transform with poles at z = 0.5 and z = 1.5. What is the ROC?

Stability from Z-Transform

All poles inside unit circle for BIBO stability.

4 min read

Inverse Z-Transform

Partial fractions, long division, contour integration.

5 min read

Z-Transform Properties

Linearity, time shift, convolution, initial/final value.

7 min read

Z-Transform Definition

ROC, properties, standard pairs.

5 min read

Inverse Z-Transform

Partial fractions, power series, residue method.

7 min read

Z-Transform Definition

Z-Transform of Standard Sequences

Contents

Z-Transform ROC

Z-Transform ROC

Q1.A causal LTI system has a Z-transform with poles at z = 0.5 and z = 1.5. What is the ROC?

Related Articles

Stability from Z-Transform

Inverse Z-Transform

Z-Transform Properties

Z-Transform Definition

Inverse Z-Transform