The z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl.

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Presentation transcript:

The z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl

Generalizing the DTFT M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl2

Complex Exponential Excitation M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl3

The Transfer Function M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl4

Systems Described by Difference Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl5

Direct Form II Realization Direct Form II realization of a discrete-time system is similar in form to Direct Form II realization of continuous-time systems A continuous-time system can be realized with integrators, summing junctions and multipliers A discrete-time system can be realized with delays, summing junctions and multipliers M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl6

Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl7

The Inverse z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl8

Existence of the z Transform Time Limited Signals M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl9

Existence of the z Transform Right- and Left-Sided Signals M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl10

Existence of the z Transform Right- and Left-Sided Exponentials M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl11

Existence of the z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl12

Existence of the z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl13

Existence of the z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl14

Some Common z Transform Pairs M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl15

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl16

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl17

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl18

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl19

The Inverse z Transform Synthetic Division M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl20

Synthetic Division The Inverse z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl21

Synthetic Division The Inverse z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl22

Synthetic Division The Inverse z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl23

Partial Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl24

Partial Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl25

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl26

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl27

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl28

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl29

z-Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl30

Inverse z Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl31

Inverse z Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl32

7/3/2015 Inverse z Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl33

The Unilateral z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl34

Properties of the Unilateral z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl35

Solving Difference Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl36

Solving Difference Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl37

Pole-Zero Diagrams and Frequency Response For a stable system, the response to a sinusoid applied at time t = 0 approaches the response to a true sinusoid (applied for all time). M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl38

Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl39

Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl40

Transform Method Comparison M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl41

Transform Method Comparison M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl42

Transform Method Comparison M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl43

Transform Method Comparison M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl44

System Response to a Sinusoid M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl45

System Response to a Sinusoid M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl46

System Response to a Sinusoid M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl47