dsp_foehu - lec 06 - the z-transform

20

Upload: amr-e-mohamed

Post on 12-Apr-2017

338 views

Category:

Engineering


1 download

TRANSCRIPT

Page 1: DSP_FOEHU - Lec 06 - The z-Transform
Page 2: DSP_FOEHU - Lec 06 - The z-Transform

otherwise 0

0nfor 1 (n)

1 (n) n

n

n

n zznxzX

otherwise 0

qnfor 1 q)-(n

q

n

n

n

n zzznxzX q)-(n

Page 3: DSP_FOEHU - Lec 06 - The z-Transform

0nfor 0

0nfor 1 (n)u

11

1 (n)

10 z

z

zzzuznxzX

n

n

n

n

n

n

0nfor 0

0nfor (n)

nn aua

0

(n) n

nn

n

nn

n

n zazuaznxzX

az

z

azazzX

n

n

10

1

1

1)(

Page 4: DSP_FOEHU - Lec 06 - The z-Transform

0nfor 0

0nfor (n)

nn nauna

0

n (n) n

nn

n

nn

n

n zazunaznxzX

2210

1

)()1(

1)(n

az

z

azazzX

n

n

0nfor 0

0nfor )cos( (n))cos(

nun

2

n)( cosnjnj ee

)}()({2

1 u(n)}n)( {cos nuenueZ njnj

jj ez

z

ez

z

2

1 u(n)}n)( {cos

1)( cos2

)( cos

)( cos21

)( cos1 u(n)}n)( {cos

2

2

21

1

zz

zz

zz

z

1)( cos2

)( s

)( cos21

)( s u(n)}n)({sin

221

1

zz

inz

zz

inz

Page 5: DSP_FOEHU - Lec 06 - The z-Transform

0

1 n

n

n

nnn azznuazXnuanx

az

z

azazzX

n

n

01

1

1

1

Page 6: DSP_FOEHU - Lec 06 - The z-Transform

111 1

n

n

n

nnn azznuazXnuanx

azza 11

...]1[... 33221133221 zazazazazazazazX

az

z

zazazX

1

1

1

1

Page 7: DSP_FOEHU - Lec 06 - The z-Transform
Page 8: DSP_FOEHU - Lec 06 - The z-Transform
Page 9: DSP_FOEHU - Lec 06 - The z-Transform
Page 10: DSP_FOEHU - Lec 06 - The z-Transform

xnZ

o RROCzXznnx o

x

nnnZ

o RROCzzXznnxo

o x(n) - 0n

xZn RROCzXnx /

nurenurenunrnxnjnj

on oo

2

1

2

1cos

Page 11: DSP_FOEHU - Lec 06 - The z-Transform
Page 12: DSP_FOEHU - Lec 06 - The z-Transform

1z :ROC assume 1

1

1

1

1

111 azza

zY

Page 13: DSP_FOEHU - Lec 06 - The z-Transform
Page 14: DSP_FOEHU - Lec 06 - The z-Transform

kdzkk zXzdA 11

1

11!

1

idw

s

ims

ms

ms

i

m wXwddw

d

dmsC

Page 15: DSP_FOEHU - Lec 06 - The z-Transform
Page 16: DSP_FOEHU - Lec 06 - The z-Transform

n8u-2

192 nunnx

n

Page 17: DSP_FOEHU - Lec 06 - The z-Transform
Page 18: DSP_FOEHU - Lec 06 - The z-Transform
Page 19: DSP_FOEHU - Lec 06 - The z-Transform
Page 20: DSP_FOEHU - Lec 06 - The z-Transform