FIR數(shù)字濾波器設(shè)計(jì)上機(jī)

FIR數(shù)字濾波器設(shè)計(jì)一、窗函數(shù)法窗函數(shù)w=hanning(N)w=hamming(N)w=blackman(N)w=kaiser(N,beta)P188例5-4Kaiser(凱澤)窗

Kaiser窗設(shè)計(jì)FIR濾波器的MATLAB函數(shù)[M,Wc,beta,ftype]=kaiserord(f,a,dev)f:表示需設(shè)計(jì)的FIR濾波器的頻帶。a:B個(gè)元素的向量,表示FIR濾波器在B個(gè)頻帶中的幅度值。一般對(duì)通帶取值為1，阻帶取值為0。dev:B個(gè)元素的向量,表示FIR濾波器在B個(gè)頻帶中的波動(dòng)值。

返回參數(shù)M及beta，分別表示FIR濾波器階數(shù)M及Kaiser窗的參數(shù)b。

返回參數(shù)Wc和ftype是函數(shù)fir1的調(diào)用參數(shù)。h=fir1(M,Wc,'ftype',window)M表示濾波器的階數(shù)。Wc表示理想FIR濾波器的B個(gè)頻帶。ftype表示濾波器的類型，缺省值為空。window是一長(zhǎng)度為N+1的向量,Hamming窗。Kaiser(凱澤)窗

獲得FIR濾波器的單位脈沖響應(yīng)wp=0.3*pi;ws=0.5*pi;As=50;N=ceil((As-7.95)/(ws-wp)/2.285)N=N+mod(N,2)beta=0.1102*(As-8.7);w=kaiser(N+1,beta);wc=(wp+ws)/2;alpha=N/2;k=0:N;hd=(wc/pi)*sinc((wc/pi)*(k-alpha));h=hd.*w';omega=linspace(0,pi,512);mag=freqz(h,[1],omega);magdb=20*log10(abs(mag));plot(omega/pi,magdb);axis([0,1,-70,0]);grid;利用MATLAB實(shí)現(xiàn)上例Wp=0.3p,Ws=0.5p，Ap=0.1dB,As=40dB。例：設(shè)計(jì)一滿足下列指標(biāo)的線性相位FIR高通濾波器。Wp=0.67p,Ws=0.53p，Ap=0.3dB,As=50dB。解:由As確定截?cái)嗨么昂瘮?shù):Hamming窗或Kaiser窗二、采用Hamming窗截?cái)?，利用MATLAB實(shí)現(xiàn)%Program:利用hamming窗設(shè)計(jì)FIR高通濾波器%filterspecificationWp=0.67*pi;Ws=0.53*pi;Ap=0.3;As=50;%determinethelengthofthefilter

N=ceil(7*pi/(Wp-Ws));N=mod(N+1,2)+N;M=N-1;fprintf(’N=%.0f\n',N);%generatewindoww=hamming(N)';例：設(shè)計(jì)一滿足下列指標(biāo)的線性相位FIR高通濾波器。Wp=0.67p,Ws=0.53p，Ap=0.3dB,As=50dB。解:由As確定截?cái)嗨么昂瘮?shù):Hamming窗或Kaiser窗二、采用Hamming窗截?cái)?，利用MATLAB實(shí)現(xiàn)%cutofffrequencyofidealhighpassfilterWc=(Wp+Ws)/2;k=0:M;hd=-(Wc/pi)*sinc(Wc*(k-0.5*M)/pi);hd(0.5*M+1)=hd(0.5*M+1)+1;h=hd.*w;omega=linspace(0,pi,512);mag=freqz(h,[1],omega);magdb=20*log10(abs(mag));plot(omega/pi,magdb);例：設(shè)計(jì)一滿足下列指標(biāo)的線性相位FIR高通濾波器。Wp=0.67p,Ws=0.53p，Ap=0.3dB,As=50dB。解:由As確定截?cái)嗨么昂瘮?shù):Hamming窗或Kaiser窗三、采用Kaiser窗截?cái)?，利用MATLAB實(shí)現(xiàn)%Program:利用Kaiser窗設(shè)計(jì)FIR高通濾波器Ap=0.3;As=50;Rp=1-10.^(-0.05*Ap);Rs=10.^(-0.05*As);f=[0.53,0.67];a=[0,1];dev=[Rp,Rs];[M,Wc,beta,ftype]=kaiserord(f,a,dev);%使濾波器為I型M=mod(M,2)+M;h=fir1(M,Wc,ftype,kaiser(M+1,beta))omega=linspace(0,pi,512);mag=freqz(h,[1],omega);plot(omega/pi,20*log10(abs(mag)));Kaiser窗設(shè)計(jì)的高通濾波器N=42,Ap=0.034dB,As=52.4dBWp=0.67p,Ws=0.53p，Ap=0.3dB,As=50dB00.10.20.30.40.50.60.70.80.91-140-120-100-80-60-40-20020利用Kaiser窗實(shí)現(xiàn)多帶濾波器若FIR濾波器有4個(gè)頻帶，其分別為0Wpf1pf2Wpf3pf4Wpf5pf6WpFIR濾波器在4個(gè)頻帶中的幅度值為a1a2a3a4(通帶取1，阻帶取0)FIR濾波器在4個(gè)頻帶中的波動(dòng)

d1

d2

d3

d4則可以利用MATLAB中的kaiserord和fir1函數(shù)實(shí)現(xiàn)f=[f1f2f3f4f5f6];a=[a1a2a3a4];dev=[d1

d2

d3

d4];[M,Wc,beta,ftype]=kaiserord(f,a,dev);h=fir1(M,Wc,ftype,kaiser(M+1,beta))例:試用Kaiser窗設(shè)計(jì)滿足下列指標(biāo)的具有2個(gè)通帶FIR濾波器。Ws1=0.1p,Wp1=0.2p，Wp2=0.4p,Ws2=0.5p,Ws3=0.6p,Wp3=0.7p,Wp4=0.8p,Ws4=0.9p,ds=0.01。f=[0.10.20.40.50.60.70.80.9];a=[0,1,0,1,0];Rs=0.01;dev=Rs*ones(1,length(a));[N,Wc,beta,ftype]=kaiserord(f,a,dev);h=fir1(N,Wc,ftype,kaiser(N+1,beta));omega=linspace(0,pi,512);mag=freqz(h,[1],omega);plot(omega/pi,20*log10(abs(mag)));xlabel('Normalizedfrequency');ylabel('Gain,db');grid;axis([01-805]);00.10.20.30.40.50.60.70.80.91-80-70-60-50-40-30-20-100NormalizedfrequencyGain,db例:試用Kaiser窗設(shè)計(jì)滿足下列指標(biāo)的具有2個(gè)通帶FIR濾波器。Ws1=0.1p,Wp1=0.2p，Wp2=0.4p,Ws2=0.5p,Ws3=0.6p,Wp3=0.7p,Wp4=0.8p,Ws4=0.9p,ds=0.01。二、頻率取樣法的MATLAB實(shí)現(xiàn)1.確定取樣點(diǎn)上的值Hd[m]2.對(duì)Hd[m]做M+1點(diǎn)IDFT即可得到h[k]%頻率取樣法設(shè)計(jì)II型線性相位低通FIRN=63;Wp=0.5*pi;m=0:(N+1)/2;Wm=2*pi*m./(N+1);mtr=floor(Wp*(N+1)/(2*pi))+2;Ad=[Wm<=Wp];Ad(mtr)=0.38;Hd=Ad.*exp(-j*0.5*N*Wm);Hd=[Hdconj(fliplr(Hd(2:(N+1)/2)))];h=real(ifft(Hd));w=linspace(0,pi,1000);H=freqz(h,[1],w);plot(w/pi,20*log10(abs(H)));grid;上例的MATLAB實(shí)現(xiàn)Wp=0.5p，Ws=0.6p。過渡點(diǎn)幅值0.38。上例的設(shè)計(jì)結(jié)果Wp=0.5p，Ws=0.6p。過渡點(diǎn)幅值0.38。利用1個(gè)過渡點(diǎn)設(shè)計(jì)的FIR低通濾波器的幅度函數(shù)一個(gè)過渡點(diǎn)幅值0.38利用1個(gè)過攤渡點(diǎn)笑設(shè)計(jì)誼的FI顫R低通救濾波矩器的符增益燃響應(yīng)阻帶衰減43顧dB上例利的設(shè)佳計(jì)結(jié)蘿果Wp=0軍.5p，Ws=0社.6p。過渡笨點(diǎn)幅大值0.識(shí)38。上例換的設(shè)獸計(jì)結(jié)色果Wp=0比.5p，Ws=0端.6p。過渡填點(diǎn)T2=0回.5震9和T1=0際.1辭1。兩個(gè)砍過渡踐點(diǎn)幅值0.烏11垃,瘋0慶.5到9利用2個(gè)過點(diǎn)渡點(diǎn)擊設(shè)計(jì)咸的FI救R低通反濾波型器的堡幅度字函數(shù)利用2個(gè)過寄渡點(diǎn)具設(shè)計(jì)頌的FI起R低通撫濾波嬸器的稻增益脖響應(yīng)阻帶衰減62綢dB上例仿的設(shè)繡計(jì)結(jié)盲果Wp=0崗.5p，Ws=0冤.6p。過渡舒點(diǎn)T2=0樸.5撫9和T1=0意.1會(huì)1。例：用頻隙率取術(shù)樣法搖設(shè)計(jì)的一個(gè)達(dá)滿足真下列槽指標(biāo)騰的I型線軍性相麗位高療通濾絮波器嶼。Ws=0魔.5p，Wp=0泊.6pM=亂32婚;W元p=駱0.東6*喘pi埋;眼m=旨0:句(M蠶+1餅)/門2;Wm兼=2相*p沈i*某m.濃/(育M+恐1)邀;mt羽r=ce錄il愧(W里p*(肺M+氧1)蔥/(紋2*叢pi概))螺;Ad橫=do堂ub憶le嬸([騙Wm>=Wp])切;Ad京(m北tr)=俗0.跑28支;Hd=A截d.南*e杯xp輝(-鞭j*謝0.控5*羅M*妻Wm邊);Hd=[Hdco握nj秒(f狡li蠅pl嘉r(品Hd泳(2歌:M諒/2賣+1郊))皆)]醋;h=re糧al將(i弱ff逃t(箭Hd))枯;w=絡(luò)li擔(dān)ns拌pa虎ce摔(0娛.1煮,p宋i,早10向00料);H=繳fr礎(chǔ)eq添z(騎h,攪[1防],訂w)驢;pl碰ot伙(w溝/p覽i,謝20思*l絹og棋10驅(qū)(a容bs避(H顏))兇);憤gr逝id性;%頻率漆取樣逮法設(shè)渴計(jì)I型線看性相北位高增通FI府R頻率抬取樣餐法設(shè)業(yè)計(jì)的秋高通俗濾波皆器幅花度函啄數(shù)00.20.40.60.811.21.41.61.82-0.200.20.40.60.811.2A(W)W/p上例逢