Download presentation

Published byDwight Hardy Modified over 4 years ago

1
Lecture #07 Z-Transform meiling chen signals & systems

2
**H = The impulse response of system H eigenvalue eigenfunction**

meiling chen signals & systems

3
meiling chen signals & systems MIT signals & systems

4
**DTFT is a special case of Z transform**

Discrete-time Fourier transform Where z is complex if DTFT is a special case of Z transform Same as FT is a special case of Laplace transform meiling chen signals & systems

5
**Let be a complex number The DTFT of a signal meiling chen**

signals & systems

6
**Laplace/inverse laplace transfrom**

The z-transform of an arbitrary signal x[n] and the inverse z-transform Notation meiling chen signals & systems

7
**Region of convergence (ROC)**

Critical question : Does the summation converge to a finite value In general that depends on the value of z Since Unique circle meiling chen signals & systems

8
meiling chen signals & systems MIT signals & systems

9
Example : Z-transform R.O.C meiling chen signals & systems

10
**Properties of Z transform**

Linearity Right shift in time Left shift in time Time Multiplication Frequency Scaling Modulation meiling chen signals & systems

11
Convolution meiling chen signals & systems

12
Initial value theorem meiling chen signals & systems

13
Final value theorem meiling chen signals & systems

14
**Some common Z transforms**

meiling chen signals & systems

15
**Example : Inverse Z-transform**

meiling chen signals & systems

16
**Example : the Z transform can be used to solve difference equations**

Taking the Z transform meiling chen signals & systems

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google