Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse...

Digital Signal ProcessingDigital Signal Processing( week 14 )( week 14 )

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

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

Z 변환

kk knxbknyany

][][][

IIR Filter IIR Filter

특 징 장점 : 급격한 차단특성을 가지는 필터를 FIR 보다 낮은 차수로 구성 단점 : “ 안정성” 고려 , 양자화 에러에 민감

IIR FilterIIR Filter

Butterworth vs. Chebyshev

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

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

Butterworth IIR Filter : Lowpass filter

참고 : buttord 함수

참고 : butter 함수

Butterworth IIR Filter

(1) impulse response

( 단위 : π)

(2) magnitude response

)( jeH

Butterworth IIR Filter : Lowpass filter frequency break point : [0 1000 1500 ~] amplitude break point : [1 1 0] Ap = 3dB, As = 10dB

: sampling freq.

단위 :Hz

Butterworth IIR Filter

)( jeH

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

Butterworth IIR Filter : Bandpass filter

(1) impulse response (2) magnitude response

( 단위 : π)

)( jeH

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

참고 : cheby1ord 함수

참고 : cheby1 함수

Chebyshev Type I IIR Filter

(1) impulse response

( 단위 : π)

(2) magnitude response

)( jeH

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

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

참고 : ellipord 함수

참고 : ellip 함수

Elliptic IIR Filter : Bandpass filter

(1) impulse response (2) impulse response

( 단위 : π)

)( jeH

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

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 ^

양자화소수점

1 1 1 0 1 1

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

양자화

소수점

1 0 1 1 1 0

1 0 1 1

bit-length 만큼 좌로 shift

소수점 이하 버림

bit-length 만큼 우로 shift

과 제과 제

작성한 M 파일과 HWP(DOC) 파일 압축

파일명 : 02_ 학번 _ 성명 .zip

수업시간 끝나기 전까지

E-mail : young220 @ paran.com

수고 하셨습니다

Digital Signal Processing ( week 14 ). Digital Image Processing LAB. IIR Filter Infinite Impulse...

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