DSP_FOEHU - Lec 06 - The z-Transform

2. otherwise0
0nfor1
(n)
1(n)
n
n
n
n
zznxzX
otherwise0
qnfor1
q)-(n
q
n
n
n
n
zzznxzX q)-(n

3. 0nfor0
0nfor1
(n)u
11
1
(n) 1
0 z
z
z
zzuznxzX
n
n
n
n
n
n
0nfor0
0nfor
(n)
n
n a
ua
0
(n)
n
nn
n
nn
n
n
zazuaznxzX
az
z
az
azzX
n
n
1
0
1
1
1
)(

4. 0nfor0
0nfor
(n)
n
n na
una
0
n(n)
n
nn
n
nn
n
n
zazunaznxzX
221
0
1
)()1(
1
)(n
az
z
az
azzX
n
n
0nfor0
0nfor)cos(
(n))cos(
n
un
2
n)(cos
njnj
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

5. 0
1
n
n
n
nnn
azznuazXnuanx
az
z
az
azzX
n
n
0
1
1
1
1

6. 1
1
11
n
n
n
nnn
azznuazXnuanx
azza 11
...]1[... 33221133221
zazazazazazazazX
az
z
za
zazX 1
1
1
1

10. x
nZ
o RROCzXznnx o
x
n
nnZ
o RROCzzXznnx
o
o
x(n)-
0n
x
Zn
RROCzXnx /
nurenurenunrnx
njnj
o
n oo
2
1
2
1
cos

12. 1z:ROCassume
1
1
1
1
1
1
11
azza
zY

14. kdzkk zXzdA 1
1
1
1
1
!
1
idw
s
ims
ms
ms
i
m wXwd
dw
d
dms
C

16. n8u-
2
1
92 nunnx
n