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Fourier Transform

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Laplace Transform

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Z-Transform

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Z-Transform of Standard Sequences

Unit step, exponential, sinusoidal z-transforms.

Darshan N

Updated: 19 March 2026

5 min read

#Signals & Systems

Standard Sequence Transforms

Test your ability to derive and identify Z-transforms of unit step, exponential, and sinusoidal sequences.

Question 1 of 3

Q1.The Z-transform of x[n] = a^n u[n] is:

Z-Transform Definition

X(z) = sum x[n]z^(-n), relation to Laplace via z=e^(sT).

6 min read

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 Definition

ROC, properties, standard pairs.

5 min read

Inverse Z-Transform

Partial fractions, power series, residue method.

7 min read

Z-Transform ROC

Z-Transform Properties

Contents

Z-Transform of Standard Sequences

Standard Sequence Transforms

Q1.The Z-transform of x[n] = a^n u[n] is:

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