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

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Presentation on theme: "The z Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl."— Presentation transcript:

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

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

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

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

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

6 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

33 7/3/2015 Inverse z Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl33

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

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

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

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

38 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

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

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

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

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

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

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

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

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

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


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