digital signal processing solutions to final 2014 edited by yang-ting justing chou confirmed by...
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Digital Signal ProcessingSolutions to Final 2014
Edited by Yang-Ting Justing ChouConfirmed by Prof. Jar-Ferr Kevin Yang
LAB: 92923 R, TEL: ext. 621E-mail: [email protected]
Page of MediaCore: http://140.116.92.181
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
Announcement
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AVG: 136.6111 STDEV:28.9780 MAX:175 Total: 185
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1.1 ( a ) Explanation
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1.1 ( b ) Explanation
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
1.1 ( c ) Explanation
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MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
1.1 ( d ) Explanation
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MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
1.2 (a) Explanation
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MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
1.2 (b) Explanation
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MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
1.3 Bilinear Transform
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)(45.1
)(1045.1
23tan
12
2
3
ms
s
Ts
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
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1.4 Transfer Functions
H1(z):HP H2(z):HPH3(z):BPH4(z):BP
HPF
BPF
LPF
LPF
BR
HPF
H5(z):HPH6(z):BPH7(z):BRH8(z):BP
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
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1.5 FFT
Decimation In Time (DIT)
][][][][
]12[]2[][
2
1
02
1
0
1
0
)12(2
1
0
22
kHWkGWrhWWrg
WrxWrxkX
kN
N
r
rkN
kN
N
r
rkN
N
r
krN
N
r
rkN
][][][][][][ 22 kHWKXWkHkGWkHkY kN
kN
kN
(a)
(b)
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
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2.1 Filter Design
5;5.0 (b)
Frequency transformation:
( )
1 1
1
j j
j j
j j
j
j
j
e ee e
e ee
ee
Filters of T1 is LPF to HPF
1
1
1, and
1j jz
Z Z e z ez
Simplest transformation:
1
111
1)(
z
zzGZ
k
k
(a)
1
1
1, and
1j jz
Z Z e z ez
1 1
j j
j j
j j
e ee e
e e
Filters of T1 is LPF to LPF
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
2.1 (c) Filter Design
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T2:T1:
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
2.2 Linear Phase Filter
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HFIR(z) = (1+b0z-1) (1+b2z-1+2z-2) (2+b1z-1+3z-2) = (1+b0z-1)(2+(b1+2b2) z-1+(b1b2+7)z-2+(2b1+3b2)z-3+6z-4) = 2+ (2b0+ b1+2b2)z-1 +(b0b1+2b0b2+b1b2+7) z-2 +(b0b1b2+7b0+2b1+3b2) z-3 +(2b0b1+3b0b2+6) z-4 +(6b0)z-5
3;7;3
1210 bbb
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
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2.3 All-pass Filter
43
321
40
302
22
111
43
321
30
22
11
1
4322
)()()1()1(
4322
))(1()(
zazzz
zazaazazaa
zazzz
zazazazzH IIR
12
)(
2
)(
3
)1(
4
)1( 00221
3
1
aaaaa
a
a
無解 !!!
1
03
13
2
2
)(
2
)(
3
)1(
4
)1(
3
2
1
0
00221
3
1
a
a
a
a
kaaaaa
a
a
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
(a)
(b) DFT8(DFT8(x8[n]))=DFT8(X[k])=8x[((-n)) 8] =[32 -32 -48 8 -24 24 -8 48]
(c)
(d)
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3.1 DFT
0]12[16][][)(15
0
16
)12(2
16
15
016
xekXkXjk
kj
k
k
12)1]([][]4[7
0
7
0
8
)4(2
8
n
n
n
nj
nxenxX
0)1]([][]16[16
0
7
0
8
)16(2
16
n
n
n
nj
nxenxX
(e)12)1]([][]8[
15
0
15
0
16
)8(2
16
n
n
n
nj
nxenxX
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
(a)
(b)
(c)
2
))][((][][][][Im][
* nxnxnxOddnykXjkY
]5.05.2,5.35.0,5.2,0,5.2,5.35.0,5.05.2,2[][ jjjjjjjny
452][8][7
0
27
0
2 n=k=
ny kY
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3.2 IDFT
]34, 23, 26, 2, 1,54,21,22[2
1][ jjjjjjny
]21, 54, 1, 2,26,23, 34,22[ jjjjjj
2
][][][Re][][][
* nxnxnxnwkXEvenkW
]2,1,4,1,2[][ nw
(d)16]0[8][][
7
0
08
7
0
wWkWk Wk=
k
k=
]2, 1,54,21,22[2
1][ jjjnw
]2, 1,54,21,22[ jjj
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
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(a)
3.3 N-Point DFT
]))2[((2]))1[((3][ NN njxnxnw
][]))[((]))[((]))1[(( )()1( kXWWmxWWmxWnx kN
kmNN
kN
kmNN
nkNN
][]))[((
]))[((]))2[((
)4
2()()4
2(
)2(4/
kXWWmxW
WmxWWnxjN
k
Nkm
NN
Nk
N
kmNN
NN
nkNN
][)23(][)23(][)
42(2 kXWWkXjWWkW
Nk
Nk
Nk
Nk
N
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
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(b) ))][((][][ nxnxng
(c)
3.3 N-Point DFT
))][((][))][((])[())])[((][( kXkXWnxWnxWnxnxn
nkN
n
nkN
n
nkN
][)(][ nxjny n
]4
[][][][)()
4(
4 NkXWnxWnxWWnxj
Nkn
Nn
nkN
n
Nn
Nnk
Nn
n
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
jj
jj
213211
0000
0000
2321row column
jj
jjj
jj
jjj
336330
43321
1012
23341
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3.4 2-D DFT
(0,0)
2001
0000
0000
1002
],[ mnx
MediaCore Lab, National Cheng Kung University, Tainan, Taiwan
Thanks for Your Attention!
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