上海交通大学：《数字信号处理 Digital Signal Processing（B）》教学资源_Handouts_ch10 FIR

Digital Signal Processing 主讲：张君 上文大

Digital Signal Processing 主讲：张君

Characteristics of practical frequency-selective filters Digital Signal Processing--FIR Digital Filter Design IH(@)l 1+61 1-81 δ1~Passband ripple 82~Stopband ripple Passband ripple p~Passband edge frequency @Stopband edge frequency Stopband Transition 82 band Qp D π Figure 10.1.2 Magnitude characteristics of physically realizable filters. 上游充通大

Digital Signal Processing—— FIR Digital Filter Design Characteristics of practical frequency-selective filters

Digital Filter Design Digital Signal Processing--FIR Digital Filter Design The filter design problem is the problem of constructing the transfer function of a filter that meets prescribed frequency response specifications. FIR Filter *advantage linear phase property ·stability disadvantage ·long filter length most computation cost IIR Filter 上游充通大学

Digital Signal Processing—— FIR Digital Filter Design Digital Filter Design The filter design problem is the problem of constructing the transfer function of a filter that meets prescribed frequency response specifications. FIR Filter advantage • linear phase property • stability disadvantage • long filter length • most computation cost IIR Filter

Digital Filter Classification Digital Signal Processing--FIR Digital Filter Design A filter's structure is probably the most common method of Digital Filter classification. That is Infinite Impulse Response Digital Filter(IIR)and Finite Impulse Response Digital Filter(FIR): bz H(z)= r=0 1+ ∑a4zt k=1 H(z)= h(n)z n=0 上浒充通大￥

Digital Signal Processing—— FIR Digital Filter Design Digital Filter Classification A filter's structure is probably the most common method of Digital Filter classification. That is Infinite Impulse Response Digital Filter(IIR) and Finite Impulse Response Digital Filter (FIR) : 0 1 1 0 ( ) 1 ( ) ( ) M r r r N k k k N n n b z H z a z H z h n z             

Ideal Filter Digital Signal Processing--FIR Digital Filter Design Lowpass H() -2π 一元 0 2π Highpass (e 0 -2元 一元 0 2w Bandpass H() -0 -2元 一元 0 2π Bandstop He -2元 一元 0 2元 Fig 10.1.1 ideal Lowpass Highpass,Bandpass Bandstop Magnitude Response 上游充通大学

Digital Signal Processing—— FIR Digital Filter Design Ideal Filter Fig 10.1.1 ideal Lowpass、Highpass、Bandpass、Bandstop Magnitude Response (e ) j H (e ) j H (e ) j H (e ) j H 0 Lowpass 0 Highpass 0 Bandpass 0 Bandstop     2π 2π 2π 2π ππππ π π π π 2π 2π 2π 2π

Ideal Filter Digital Signal Processing--FIR Digital Filter Design Dl@)- -8 |o≤0 .The frequency characteristics are ，o.≤o≤π periodic and even functions. dp(k)=sin(@k)/() .Phase are all considered zero. D:@)= ≤0 如 .Sharp edges at cutoff frequencies dnp(k)=6(k)-sin(@k)/(k) Infinite length sequences are all even (or symmetrical)and real-valued 1, 0。≤⊙≤0 Dgp(@)= o,≤⊙≤π functions. 0 0≤ld≤oa .High pass filter equals to all pass filter dpp(k)= sin(;k)-sin(@k) minus low pass filter 水 0 0。≤⊙≤0 Band pass equals to one low pass filter o,≤⊙≤π minus the other low pass filter. 0≤o≤oa Band stop filter equals to all pass filter dps(k)=5(k)- sin(k)-sin(@k 水 minus band pass filter 上游克通大

Digital Signal Processing—— FIR Digital Filter Design Ideal Filter •The frequency characteristics are periodic and even functions. •Phase are all considered zero. •Sharp edges at cutoff frequencies •Infinite length sequences are all even (or symmetrical) and real-valued functions. •High pass filter equals to all pass filter minus low pass filter •Band pass equals to one low pass filter minus the other low pass filter. •Band stop filter equals to all pass filter minus band pass filter

Ideal Filter Digital Signal Processing--FIR Digital Filter Design Differentiator .The frequency characteristics are D(@)=jo periodic and odd functions. dlk)=cos(a）_sin() .Only imaginary part occurs. k 2 .Infinite length sequences are both odd (or antisymmetrical)and real- Hilbert transformer valued functions. D(o）=-jsign(o) Both filters have d(0)=0. d(k)=1-cos(k) .All have linear phase property. 永 ↑D(O)j D(o)j differentiator ① 0 一π 0 Hilbert transformer 上浒充通大

Digital Signal Processing—— FIR Digital Filter Design Ideal Filter •The frequency characteristics are periodic and odd functions. •Only imaginary part occurs. •Infinite length sequences are both odd (or antisymmetrical) and real￾valued functions. •Both filters have d(0)=0. •All have linear phase property. Differentiator Hilbert transformer

Design of linear-phase FIR filters using windows Digital Signal Processing--FIR Digital Filter Design H,(o)=∑h,(n)em h(n)=w(n)d (n -M) 1=0 h,(m)=2元H,(@)edo @)=nww-aewpw)g aamro-ale- h(n）=ha(n)w(n） (time domain） h(n),n=0,1,,M-1 0, otherwise 上游充通大

Digital Signal Processing—— FIR Digital Filter Design Design of linear-phase FIR filters using windows h(n)= w(n)d(n − M)

Rectangular windowing function Digital Signal Processing--FIR Digital Filter Design .Its spectrum W(w) w(n)= 0≤n≤N-1 >The period is w=2T. 0 otherwise >The height of the main lobe is N-1 m,(e)= 1-w N and its bottom width is 4T/N. 1=0 1-1 >The height of the first side lobe N is about 2N/3TTat w=3TT/N. W(o)= ∑ea sin(No/2 e-j(N-1)o/2 n=0 sin(@/2) >The attenuation of side lobe is approximately 13dB. H(o)= in(No/2) >The zero-cross points are sim(o/2） ωk=2kTN,k=士1，±2，， ↑H(o) ±(N-1). .Frequency leakage:because of sharp transition of window edges. .Frequency resolution:because of the 2T/N3dB-width of the main lobe. 上浒究通大粤

Digital Signal Processing—— FIR Digital Filter Design Rectangular windowing function •Its spectrum W(ω) The period is ω=2π. The height of the main lobe is N and its bottom width is 4π/N. The height of the first side lobe is about 2N/3πat ω=3π/N. The attenuation of side lobe is approximately 13dB. The zero-cross points are ωk=2kπ/N, k=±1, ±2,…, ±(N-1). •Frequency leakage: because of sharp transition of window edges. •Frequency resolution: because of the 2π/N3dB-width of the main lobe

Design of linear-phase FIR filters using windows Digital Signal Processing--FIR Digital Filter Design dk)=」Dw) -M≤k≤M 2π d=[d-M,...,d-2,d-1,do,di,d2,...,dm] h=d=[ho,...,hm-2,hM-1,hM,hM+1,hM+2,...,h2m] h(n)=d(n-M),n=0,1,.,N-1 rectangular ◆dk) ◆h(n) rectangular window window w(n) ●● ●最 …-5-4-3-2-1012345…k -2-10123456789…n 上府元通大￥

Design of linear-phase FIR filters using windows Digital Signal Processing—— FIR Digital Filter Design