- Home/
- GATE ELECTRONICS/
- GATE EC/
- Article
Z-Transform-1 Study Notes for GATE Electronics and Communication Engineering Exam
By BYJU'S Exam Prep
Updated on: September 25th, 2023
In this article, you will find the Z-Transform-1 which will cover the topic as Z-Transform, Region of Convergence (ROC), Summary of ROC of Discrete-Time Signals for the sequences, Characteristic Families of Signals and Corresponding ROC, Summary of Properties of z- Transform.
Z-Transform
- Computation of the Z-transform for discrete-time signals.
- Enables analysis of the signal in the frequency domain.
- Z-Transform takes the form of a polynomial.
- Enables interpretation of the signal in terms of the roots of the polynomial.
- z−1 corresponds to a delay of one unit in the signal.
The Z – Transform of a discrete time signal x[n] is defined as
where z = r.ejω
- The discrete-time Fourier Transform (DTFT) is obtained by evaluating Z-Transform at z = ejω.
- The z-transform defined above has both sided summation. It is called bilateral or both sided Z-transform.
Unilateral (one-sided) z-transform
- The unilateral z-transform of a sequence x[n] is defined as
