Download presentation

1
**Z- Transform and Its Properties**

Dr. Wajiha Shah

2
The z-Transform Given the causal sequence {x[1], x[2], …., x[k],….}, its z-transform is defined as The variable z may be regarded as a time delay operator

3
**Example Find the z-transform of the sequence x = {1, 1, 3, 2, 0, 4}**

Solution:

4
**Exercise Find the z-transform of the following sequences:**

(b) {0, 0, 0, 1, 1, 1, 0, 0, 0, . . .} (c) {0, 2−0.5, 1, 2−0.5, 0, 0, 0, . . .}

5
**Z-Transform of Standard Discrete-Time Signals**

Unit Impulse Function A discrete time impulse Shown in the Fig. is defined as The z-Transform of δ(k) is X(z) = 1

6
**Sampled Step Sampled Step A sampled step function is shown in the Fig.**

Mathematically, it is defined as The z-Transform of u(k) is computed as

7
**Exponential Exponential:**

A sampled exponential function is shown in the Fig. Mathematically, it is defined as The z-Transform of x(k) is computed as

8
**Properties of z-Transform**

Linearity Let x1(k) ,x2(k) , .... be discrete time sequences and a1, a2, …. be constants, then according to this property Example: Find z-Transform of x(k) = 2u(k) + 4δ(k), where u(k) is a unit step sequence and k = 0, 1, 2, …. Solution:

9
**Contd… • Time Delay z[x(k D)]= z X(z) where D denotes time delay.**

Proof: By definition Let m = k-D or k = m+D

10
Contd… Example Find the z-transform of the causal sequence Solution:

11
Contd…

12
Contd…

13
Contd…

14
Contd…

15
**Inverse of the z-Transform**

16
Contd…

17
Contd…

18
Contd…

19
Contd…

21
Contd…

22
Contd…

23
Contd…

24
Contd…

25
Contd…

26
Convolution Sum

27
Contd…

28
Contd…

29
Transfer Function

30
Contd…

31
Contd…

Similar presentations

OK

ECE 8443 – Pattern Recognition EE 3512 – Signals: Continuous and Discrete Objectives: Convolution Definition Graphical Convolution Examples Properties.

ECE 8443 – Pattern Recognition EE 3512 – Signals: Continuous and Discrete Objectives: Convolution Definition Graphical Convolution Examples Properties.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on area of parallelogram using vectors Ppt on case study of drought in india Ppt on unemployment in india free download Ppt on philosophy of swami vivekananda Download ppt on mineral and power resources Ppt on conservation of environmental degradation Ppt on global warming solutions Ppt on artificial intelligence in electrical engineering Ppt on carburetor systems Ppt on atrial septal defect surgery