49
SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES) MA6351 /TPDE UNIT V Page 1 UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS

UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 1

UNIT V – Z- TRANSFORMS AND DIFFERENCE EQUATIONS

Page 2: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 2

Page 3: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 3

Page 4: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 4

Page 5: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 5

Page 6: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 6

Page 7: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 7

Page 8: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 8

Page 9: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 9

Page 10: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 10

Page 11: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 11

Page 12: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 12

Page 13: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 13

Page 14: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 14

Page 15: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 15

Page 16: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 16

Page 17: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 17

Page 18: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 18

Page 19: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 19

Page 20: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 20

Page 21: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 21

Page 22: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 22

Page 23: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 23

Page 24: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 24

Page 25: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 25

Page 26: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 26

Page 27: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 27

Page 28: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 28

Page 29: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 29

Page 30: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 30

Page 31: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 31

Page 32: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 32

Page 33: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 33

Page 34: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 34

Page 35: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 35

Page 36: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 36

Page 37: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 37

Page 38: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 38

Page 39: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 39

Page 40: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 40

Page 41: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 41

Page 42: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 42

Page 43: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 43

Page 44: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 44

Page 45: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 45

Page 46: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 46

Page 47: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 47

Page 48: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 48

Page 49: UNIT V Z- TRANSFORMS AND DIFFERENCE EQUATIONS · 2018. 7. 19. · sri vidya college of engineering and technology, virudhunagar co urse material (lecture notes) ma6351 /tpde unit

SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR COURSE MATERIAL (LECTURE NOTES)

MA6351 /TPDE UNIT V Page 49