digital signal processing ( week 14 ). digital image processing lab. iir filter infinite impulse...
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![Page 1: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/1.jpg)
Digital Signal ProcessingDigital Signal Processing( week 14 )( week 14 )
![Page 2: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/2.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter IIR Filter
Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력 및 출력 필요
⇒ 출력이 입력으로 Feedback 됨
⇒ Recursive Filter 구조
![Page 3: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/3.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
FIR filterFIR filter
InputInputSignalSignal
OutputOutputSignalSignalIIR filterIIR filter
x[n] y[n]h[n]
초기 정지 조건 (i.r.c) 만족 ⇒ LTI 시스템
X(z) Y(z)H(z)
][*][][ nxnhny )()()( zXzHzY
)(
)()(
zX
zYzH
Z 변환
M
kk
N
kk knxbknyany
01
][][][
![Page 4: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/4.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter IIR Filter
특 징 장점 : 급격한 차단특성을 가지는 필터를 FIR 보다 낮은 차수로 구성 단점 : “ 안정성” 고려 , 양자화 에러에 민감
![Page 5: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/5.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR FilterIIR Filter
Butterworth vs. Chebyshev
![Page 6: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/6.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter DesignIIR Filter Design
LPF 를 위한 Matlab 함수들[b, a] = butter(N, wn);[b, a] = cheby1(N, Rp, wn);[b, a] = cheby2(N, As, wn);[b, a] = ellip(N, Rp, As, wn);
buttord, cheblord, cheb2ord, ellipord, bilinear, impinvar
![Page 7: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/7.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제1) 1)
Butterworth IIR Filter : Lowpass filter frequency break point : [0 0.2 0.3 1] amplitude break point : [1 1 0 0] Ap = 3dB, As = 10dB
단위 :π
![Page 8: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/8.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제1) 1)
Butterworth IIR Filter : Lowpass filter
![Page 9: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/9.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제1) 1)
참고 : buttord 함수
![Page 10: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/10.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제1) 1)
참고 : butter 함수
![Page 11: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/11.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제1) 1)
Butterworth IIR Filter
(1) impulse response
( 단위 : π)
(2) magnitude response
)( jeH
![Page 12: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/12.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제2) 2)
Butterworth IIR Filter : Lowpass filter frequency break point : [0 1000 1500 ~] amplitude break point : [1 1 0] Ap = 3dB, As = 10dB
: sampling freq.
sf
단위 :Hz
![Page 13: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/13.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제2) 2)
Butterworth IIR Filter
)( jeH
![Page 14: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/14.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제3) 3)
Butterworth IIR Filter : Bandpass filter frequency break point : [0 0.3 0.7 1] amplitude break point : [0 1 1 0] Ap = 3dB, As = 10dB
단위 :π
![Page 15: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/15.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제3) 3)
Butterworth IIR Filter : Bandpass filter
![Page 16: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/16.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제3) 3)
Butterworth IIR Filter : Bandpass filter
(1) impulse response (2) magnitude response
( 단위 : π)
)( jeH
![Page 17: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/17.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제4) 4)
Chebyshev Type I IIR Filter : Lowpass filter frequency break point : [0 0.2 0.3 1] amplitude break point : [1 1 0 0] Ap = 3dB, As = 10dB
단위 :π
![Page 18: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/18.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제4) 4)
참고 : cheby1ord 함수
![Page 19: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/19.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제4) 4)
참고 : cheby1 함수
![Page 20: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/20.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제4) 4)
Chebyshev Type I IIR Filter
![Page 21: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/21.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제4) 4)
Chebyshev Type I IIR Filter
(1) impulse response
( 단위 : π)
(2) magnitude response
)( jeH
![Page 22: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/22.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제5) 5)
Chebyshev Type 1 IIR Filter : Bandpass Filter 예제 3, 예제 4 참고
Chebyshev Type 2 IIR Filter : Lowpass Filter 예제 4 참고
Chebyshev Type 2 IIR Filter : Bandpass Filter 예제 5 참고
![Page 23: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/23.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제6) 6)
Elliptic IIR Filter : Bandpass filter frequency break point : [0 0.3 0.7 1] amplitude break point : [0 1 1 0] Ap = 3dB, As = 10dB
단위 :π
![Page 24: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/24.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제6) 6)
참고 : ellipord 함수
![Page 25: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/25.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제6) 6)
참고 : ellip 함수
![Page 26: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/26.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제6) 6)
Elliptic IIR Filter : Bandpass filter
![Page 27: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/27.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
IIR Filter Design (IIR Filter Design ( 예제예제6) 6)
Elliptic IIR Filter : Bandpass filter
(1) impulse response (2) impulse response
( 단위 : π)
)( jeH
![Page 28: Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse Response(IIR) filter 현재의 출력 계산을 위해 과거 ( 이전 ) 의 입력](https://reader036.vdocuments.net/reader036/viewer/2022081512/56649ec65503460f94bd11a8/html5/thumbnails/28.jpg)
Digital Image Processing Digital Image Processing LAB.LAB.
양자화 에러양자화 에러
Finite Word Length Effect 필터의 계수값을 한정된 수의 bit 로 표현할 때 발생하는 에러가 필터
성능에 미치는 영향
대 책1) Word length 증가2) 연산의 형태3) 양자화 방법4) 필터의 구조 변경
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Digital Image Processing Digital Image Processing LAB.LAB.
양자화 에러양자화 에러
필터 계수 양자화
양자화 에러
양자화 이후 spec. 만족 여부 확인
(∵ 계수 ak 를 양자화해서 ak 로 바뀌면 시스템의 모든 pole 에 영향을 받음 )
ka kkk aaa ^
kb kkk bbb ^
양자화
양자화where, Δak, Δbk : 양자화 에러
^
kkk aaa ^
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Digital Image Processing Digital Image Processing LAB.LAB.
양자화 에러양자화 에러
양자화소수점
1 1 1 0 1 1
1 1 1 0 1 1
1 1 1 0
1 1 1 0
bit-length 만큼 좌로 shift
소수점 이하 버림
( 정수부 길이 - bit-length) 만큼 우로 shift
1 1 1 0 1 1
정수부의 길이 구함
3.6875
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Digital Image Processing Digital Image Processing LAB.LAB.
양자화 에러양자화 에러
양자화
소수점
1 0 1 1 1 0
1 0 1 1 1 0
1 0 1 1
1 0 1 1
bit-length 만큼 좌로 shift
소수점 이하 버림
bit-length 만큼 우로 shift
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Digital Image Processing Digital Image Processing LAB.LAB.
과 제과 제
작성한 M 파일과 HWP(DOC) 파일 압축
파일명 : 02_ 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