Digital Signal Processing ( week 9 )
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Transcript of Digital Signal Processing ( week 9 )
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Digital Signal ProcessingDigital Signal Processing( week 9 )( week 9 )
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Digital Image Processing Digital Image Processing LAB.LAB.
FIR filterFIR filter
InputInputSignalSignal
OutputOutputSignalSignal
SystemSystem(filter)(filter)
x[n] y[n]
X(ejw) Y(ejw)
h[n]H(ejw)
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Digital Image Processing Digital Image Processing LAB.LAB.
FIR filterFIR filter
InputInputSignalSignal
OutputOutputSignalSignalLTI(FIR)LTI(FIR)
x[n] y[n]h[n]
][..]1[][][][ 100
Mnbnbnbknbnh M
M
kk
⇒ (i) 유한 길이 임펄스 응답 (ii) b0=h[0], b1=h[1], .. , bM=h[M]
][][..]1[]1[][]0[][][][*][][0
MnxMhnxhnxhknxkhnxnhnyM
k
필터 계수 {bk} = 임펄스 응답 {h[k]}
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Digital Image Processing Digital Image Processing LAB.LAB.
주파수 응답주파수 응답
정 의
FIR 필터의 주파수 응답
크기 위상 고유 주파수
M
k
kjj ekheH0
][)(
][nh )( jweHDTFT
: 주파수 응답^
F I RF I R
h[n]
njj eAe 0
njeHjnj eeeHA
nj0
00 ))(()(
A
0̂
|)(| 0
njeHA
)( 0
njeH 0̂ ( 고정 )
( 변형 )
( 변형 )
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Digital Image Processing Digital Image Processing LAB.LAB.
주파수 응답 주파수 응답
특 성 주파수 응답과 차분 방정식의 관계
는 주기신호 ( 주기 : 2π))(jeH
시간 영역 주파수 영역(delay) (modulation)
δ[n]
δ[n-1]
δ[n-2]
je 2je
1
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Digital Image Processing Digital Image Processing LAB.LAB.
주파수 응답 주파수 응답
특 성 conjugate symmetry ( 공액대칭 )
주파수 응답의 스펙트럼
⇒ 의 주파수 성분 분포가 그 필터의 주파수 특성을 결정)(jeH
bk = b*k
h[k] = h*[k])(
jeH )(*
jeH=
|)(|jeH
)(
jeH
|)(|
jeH
)(
jeH
=
=
: 우대칭
: 기대칭
)}(Re{jeH
)}(Im{jeH
)}(Re{
jeH
)}(Im{
jeH
=
=
: 우대칭
: 기대칭
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 1)1. Start Matlab
2. Insert CD
3. Add path “spfirst”
4. “ dconvdemo ” typing in Command window
5. Pez Tutorial Demo
6. zplane 실습
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 1)
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 2)1. Start Matlab
2. Insert CD
3. Add path “spfirst”
4. “ DLTIdemo ” typing in Command window
5. Pez Tutorial Demo
6. zplane 실습
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 2)
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 3) 3-Point Averaging Filter
다음을 만족하는 sinusoid 신호의 100 개 샘플을 이용
(1) x[n], y[n] 의 그래프를 그리시오 .
(2) 주파수 응답 (Magnitude, Phase) 의 그래프를 그리시오 .
]2[3
1]1[
3
1][
3
1][ nnnnh
)*08.0cos(][ nnx
LTILTIh[n]h[n]
x[n] y[n]
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
참 고 : FIRFILT 함수
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 3) 3-Point Averaging Filter (1)
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Digital Image Processing Digital Image Processing LAB.LAB.
MatlabMatlab
EX 3) 3-Point Averaging Filter (2)
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Digital Image Processing Digital Image Processing LAB.LAB.
EX 4) 2-point Averaging Filter
Frequency Response
]1[2
1][
2
1][ nxnxny )(][ jwnAenx
))1(()(
2
1
2
1][ njwjwn AeAeny
}1{2
1)( jwjwn eAe
}1{2
1)( jwjw eeH
MatlabMatlab
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Digital Image Processing Digital Image Processing LAB.LAB.
EX 4) 2-point Averaging Filter
MatlabMatlab
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Digital Image Processing Digital Image Processing LAB.LAB.
실습실습
First-Difference Filter
다음 filter 를 이용하여 Filtering 을 하시오 이 필터를 First-Difference Filter 라고 한다 .
Frequency Response (Magnitude, Phase) 를 구하시오 .
다음을 만족하는 Sinusoid 신호의 50 개 sample 을 이용
y[n] 의 출력 파형을 그리시오
]1[5][5][ nxnxny
,7A ,3 125.0
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Digital Image Processing Digital Image Processing LAB.LAB.
과 제과 제
작성한 M 파일과 HWP(DOC) 파일 압축
파일명 : 04_ 학번 _ 성명 .zip
수업시간 끝나기 전까지
E-mail : young220 @ paran.com
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Digital Image Processing Digital Image Processing LAB.LAB.
수고 하셨습니다