實(shí)驗(yàn)6FIR濾波器設(shè)計(jì)說明

.用長度為21的漢寧窗設(shè)計(jì)一個數(shù)字FIR差分器,并繪制其時域和頻率的響應(yīng)波形。n.利用漢寧窗設(shè)計(jì)一個長度為25的數(shù)字希爾伯特變換器,并繪制它的時域和頻域的響應(yīng)波形。p.FIR數(shù)字低通濾波器的技術(shù)指標(biāo)為：ωp=0.2π,ωst=0.3π,δ1=0.25dB,δ2=50dB。利用頻率采樣方法設(shè)計(jì)FIR數(shù)字濾波器,并繪制濾波器的單位沖激響應(yīng)、幅度頻率響應(yīng)的波形。q.用窗函數(shù)法設(shè)計(jì)一個線性相位的FIR數(shù)字低通濾波器,其技術(shù)指標(biāo)為：ωp=0.2π,ωst=0.4π,δ1=0.25dB,δ2=50dB。<1>求濾波器的單位抽樣響應(yīng)、頻率響應(yīng),并繪制波形。<2>對該濾波器輸入一個寬度為10的矩形序列,求濾波器的輸出信號,并繪制相應(yīng)的波形圖。測試記錄分析結(jié)論

理論與實(shí)驗(yàn)值相符?！埠蟾酱a〕小結(jié)認(rèn)真復(fù)習(xí)FIR數(shù)字濾波器的基本概念,線性相位FIR濾波器的條件和特點(diǎn)、幅度函數(shù)特點(diǎn)、零點(diǎn)位置的基本特點(diǎn)與性質(zhì)；窗函數(shù)設(shè)計(jì)法的基本概念與方法,各種窗函數(shù)的性能和設(shè)計(jì)步驟,線性相位FIR低通、高通、帶通和帶阻濾波器的設(shè)計(jì)方法,頻率采樣設(shè)計(jì)法的基本概念和線性相位的實(shí)現(xiàn)方法。以下由實(shí)驗(yàn)教師填寫記事評議

成績評定

平時成績_______實(shí)驗(yàn)報(bào)告成績________綜合成績_________指導(dǎo)教師簽名：代碼：wp=0.2*pi;ws=0.4*pi;tr_width=ws-wp;M=ceil<6.6*pi/tr_width>+1;n=[0:1:M-1];wc=<ws+wp>/2;hd=ideal_lp<wc,M>;w_ham=<hamming<M>>';h=hd.*w_ham;[db,mag,pha,H,w]=freqz_m3<h,[1]>;delta_w=2*pi/1000;Rp=-<min<db<1:1:wp/delta_w+1>>>;As=-round<max<db<ws/delta_w+1:1:501>>>;figure<1>subplot<221>stem<n,hd>;title<'IdealImpulseRresponse'>axis<[0M-1-0.10.3]>;xlabel<'n'>;ylabel<'hd<n>'>subplot<222>stem<n,w_ham>;title<'HammingWindow'>axis<[0M-101.1]>;xlabel<'n'>;ylabel<'w<n>'>subplot<223>stem<n,h>;title<'ActualImpuseResponse'>axis<[0M-1-0.10.3]>;xlabel<'n'>;ylabel<'h<n>'>subplot<224>plot<w/pi,db>;title<'MagnitudeResponseindb'>;gridaxis<[01-10010]>;xlabel<'frequencein\piunit'>;ylabel<'decibels'>%solutionofproblem<b>Rn=stepseq<0,0,9>n=0:1:9dw=w<2>-<1>w=[-fliplr<w>,w<2:501>]H=[fliplr<H>,H<2:501>]xw=Rn*<exp<-j>>.^<n'*w>answ=H.*xwRnn=answ*exp<-j>.^<w'*n>*dw/<2*pi>figure<2>subplot<221>stem<n,Rn>xlabel<'n'>;ylabel<'Rn'>;title<'inputrectanglesignalinT-domain'>subplot<222>stem<w/pi,xw>xlabel<'w/\pi'>;ylabel<'Rw'>;title<'inputrectanglesignalinF-domain'>subplot<223>plot<w/pi,abs<answ>>xlabel<'w/\pi'>;ylabel<'MagnitudeofH<w>'>;title<'outputsignalinF-domainafterfilteration'>subplot<224>stem<n,abs<Rnn>>xlabel<'n'>;ylabel<'Rnn'>;title<'outputsignalinT-domainafterfilteration'>M=25;alpha=<M-1>/2;n=0:M-1;hd=<2/pi>*<<sin<<pi/2>*<n-alpha>>.^2>./<n-alpha>>;hd<alpha+1>=0;w_han=<hann<M>>';h=hd.*w_han;[Hr,w,P,L]=Hr_Type3<h>;subplot<2,2,1>;stem<n,hd>;title<'IdealImpulseResponse'>axis<[-1M-1.21.2]>;xlabel<'n'>;ylabel<'hd<n>'>;subplot<2,2,2>;stem<n,w_han>;title<'HannWindow'>axis<[-1M01.2]>;xlabel<'n'>;ylabel<'w<n>'>subplot<2,2,3>;stem<n,h>;title<'ActualImpulseResponse'>axis<[-1M-1.21.2]>;xlabel<'n'>;ylabel<'h<n>'>w=w';Hr=Hr';w=[-fliplr<w>,w<2:501>];Hr=[-fliplr<Hr>,Hr<2:501>];subplot<2,2,4>;plot<w/pi,Hr>;title<'AmplitudeResponse'>;grid;xlabel<'frequencyinpiunits'>;ylabel<'Hr'>;axis<[-11-1.11.1]>;M=20;alpha=<M-1>/2;l=0:M-1;wl=<2*pi/M>*l;Hrs=[1,1,1,zeros<1,15>,1,1];%IdealAmpRessampledHdr=[1,1,0,0];wdl=[0,0.25,0.25,1];%IdealAmpResforplottingk1=0:floor<<M-1>/2>;k2=floor<<M-1>/2>+1:M-1;angH=[-alpha*<2*pi>/M*k1,alpha*<2*pi>/M*<M-k2>];H=Hrs.*exp<j*angH>;h=real<ifft<H,M>>;[db,mag,pha,grd,w]=freqz_m<h,1>;[Hr,ww,a,L]=Hr_Type2<h>;subplot<2,2,1>;plot<wl<1:11>/pi,Hrs<1:11>,'o',wdl,Hdr>;axis<[0,1,-0.1,1.1]>;title<'FrequencySamples:M=20'>xlabel<'frequencyinpiunits'>;ylabel<'Hr<k>'>;subplot<2,2,2>;stem<l,h>;axis<[-1,M,-0.1,0.3]>title<'ImpulseResponse'>;xlabel<'n'>;ylabel<'h<n>'>;subplot<2,2,3>;plot<ww/pi,Hr,wl<1:11>/pi,Hrs<1:11>,'o'>;axis<[0,1,-0.2,1.2]>;title<'AmplitudeResponse'>xlabel<'frequencyinpiunits'>;ylabel<'Hr<w>'>subplot<2,2,4>;plot<w/pi,db>;axis<[0,1,-60,10]>;gridtitle<'MagnitudeResponse'>;xlabel<'frequencyinpiunits'>;ylabel<'Decibels'>;Wpl=0.2*pi;Wph=0.8*pi;Wsl=0.4*pi;Wsh=0.6*pi;tr_width=min<<Wsl-Wpl>,<Wph-Wsh>>;M=ceil<6.2*pi/tr_width>n=0:1:M-1;Wcl=<Wsl+Wpl>/2;Wch=<Wsh+Wph>/2;hd=ideal_bs<Wcl,Wch,M>;w_ham=<hanning<M>>';h=hd.*w_ham;[db,mag,pha,w]=freqz_m2<h,[1]>;delta_w=2*pi/1000;Ap=-<min<db<1:1:Wpl/delta_w+1>>>As=-round<max<db<Wsl/delta_w+1:1:Wsh/delta_w+1>>>subplot<221>stem<n,hd>;title<'IdealImpulseRresponse'>axis<[0M-1-0.10.7]>;xlabel<'n'>;ylabel<'hd<n>'>subplot<222>stem<n,w_ham>;title<'HammingWindow'>axis<[0M-101.1]>;xlabel<'n'>;ylabel<'w<n>'>subplot<223>stem<n,h>;title<'ActualImpuseResponse'>axis<[0M-1-0.10.7]>;xlabel<'n'>;ylabel<'h<n>'>subplot<224>plot<w/pi,db>;title<'MagnitudeResponseindb'>;gridaxis<[01-10010]>;xlabel<'frequencein\piunit'>;ylabel<'decibels'>;clearallfigureWpl=0.2*pi;Wph=0.8*pi;Wsl=0.4*pi;Wsh=0.6*pi;tr_width=min<<Wsl-Wpl>,<Wph-Wsh>>;M=ceil<6.2*pi/tr_width>n=0:1:M-1;Wcl=<Wsl+Wpl>/2;Wch=<Wsh+Wph>/2;hd=ideal_bs<Wcl,Wch,M>;w_ham=<hanning<M>>';h=hd.*w_ham;[db,mag,pha,w]=freqz_m2<h,[1]>;delta_w=2*pi/1000;Ap=-<min<db<1:1:Wpl/delta_w+1>>>As=-round<max<db<Wsl/delta_w+1:1:Wsh/delta_w+1>>>subplot<221>stem<n,hd>;title<'IdealImpulseRresponse'>axis<[0M-1-0.10.7]>;xlabel<'n'>;ylabel<'hd<n>'>subplot<222>stem<n,w_ham>;title<'HammingWindow'>axis<[0M-101.1]>;xlabel<'n'>;ylabel<'w<n>'>subplot<223>stem<n,h>;title<'ActualImpuseResponse'>axis<[0M-1-0.10.7]>;xlabel<'n'>;ylabel<'h<n>'>subplot<224>plot<w/pi,db>;title<'MagnitudeResponseindb'>;gridaxis<[01-10010]>;xlabel<'frequencein\piunit'>;ylabel<'decibels'>;figurews1=0.2*pi;wp1=0.35*pi;ws2=0.8*pi;wp2=0.65*pi;Ap=60;Rp=1;tr_width=min<<wp1-ws1>,<ws2-wp2>>;M=ceil<11*pi/tr_width>;n=[0:1:M-1];wc1=<ws1+wp1>/2;wc2=<wp2+ws2>/2;hd=ideal_lp<wc2,M>-ideal_lp<wc1,M>;w_bla=<blackman<M>>';h=hd.*w_bla;[H,W]=freqz<h,1>;subplot<2,2,1>;stem<n,hd>;title<'àí????3?3é?ù'>;subplot<2,2,2>;stem<n,w_bla>;title<'2?à3???ü′°'>;subplot<2,2,3>;stem<n,h>;title<'êμ?ê??3?3é?ù'>;subplot<2,2,4>;plot<W/pi,20*log10<abs<H>>>;title<'·ù?è?ìó|￡¨db￡?'>;clearallfigurews1=0.2*pi;wp1=0.4*pi;ws2=0.8*pi;wp2=0.6*pi;Ap=60;Rp=1;tr_width=min<<wp1-ws1>,<ws2-wp2>>;M=ceil<11*pi/tr_width>;n=[0:1:M-1];wc1=<ws1+wp1>/2;wc2=<wp2+ws2>/2;hd=ideal_lp<wc2,M>-ideal_lp<wc1,M>;w_bla=<hamming<M>>';h=hd.*w_bla;[H,W]=freqz<h,1>;subplot<2,2,1>;stem<n,hd>;title<'àí????3?3é?ù'>;subplot<2,2,2>;stem<n,w_bla>;title<'o￡?÷′°'>;subplot<2,2,3>;stem<n,h>;title<'êμ?ê??3?3é?ù'>;subplot<2,2,4>;plot<W/pi,20*log10<abs<H>>>;title<'·ù?è?ìó|￡¨db￡?'>;clearallfigurews1=0.2*pi;wp1=0.4*pi;ws2=0.8*pi;wp2=0.6*pi;Ap=20;Rp=1;tr_width=min<<wp1-ws1>,<ws2-wp2>>;M=ceil<11*pi/tr_width>;n=[0:1:M-1];wc1=<ws1+wp1>/2;wc2=<wp2+ws2>/2;hd=ideal_lp<wc2,M>-ideal_lp<wc1,M>;w_bla=<boxcar<M>>';h=hd.*w_bla;[H,W]=freqz<h,1>;subplot<2,2,1>;stem<n,hd>;title<'àí????3?3é?ù'>;subplot<2,2,2>;stem<n,w_bla>;title<'??D?′°'>;subplot<2,2,3>;stem<n,h>;title<'êμ?ê??3?3é?ù'>;subplot<2,2,4>;plot<W/pi,20*log10<abs<H>>>;title<'·ù?è?ìó|￡¨db￡?'>;clearallfigureAs=55;ws=11*pi/27;wp=15*pi/27;tr_width=wp-ws;%????1y?é′?M=ceil<<As-7.95>*2*pi/<14.36*tr_width>+1>+1;%°′?-?ó′°??????2¨?÷μ?3¤?èdisp<['??2¨?÷μ?3¤?è',num2str<M>]>;beta=0.1102*<As-8.7>;%?????-?ó′°μ?beta?μn=[0:1:M-1];disp<['??D??à????2¨?÷',num2str<beta>]>;w_kai=<kaiser<M,beta>>';%?ó?-?ó′°oˉêywc=<ws+wp>/2;hd=ideal_lp<pi,M>-ideal_lp<wc,M>;%?óàí????3??ìó|h=hd.*w_kai;[db,mag,pha,grd,w]=freqz_m<h,[1]>;delta_w=2*pi/1000;Rp=-<min<db<wp/delta_w+1:1:501>>>;disp<['êμ?êí¨′?2¨?ˉ?a',num2str<Rp>]>;As=-round<max<db<1:1:ws/delta_w+1>>>;disp<['×?D?×è′??￥???a?',num2str<As>]>;subplot<2,2,1>;stem<n,hd>;title<'àí????3??ìó|'>;axis<[0M-1-0.40.8]>;ylabel<'hd<n>'>;subplot<2,2,2>;stem<n,w_kai>;title<'?-?ó′°'>;axis<[0M-101.1]>;ylabel<'wd<n>'>;subplot<2,2,3>;stem<n,h>;title<'êμ?ê??3??ìó|'>;axis<[0M-1-0.40.8]>;xlabel<'n'>;ylabel<'h<n>'>;subplot<2,2,4>;plot<w/pi,db>;title<'?·ù?è?ìó|/dB'>;axis<[01-10010]>;grid;xlabel<'ò?pi?aμ￥??μ??μ?ê'>;ylabel<'?·?±′êy/dB'>;clearallfigure%?úmatlab?DD??¨oˉêyg￡?′ú??è???￡oWp=0.6*pi;Ws=0.4*pi;tr_width=Wp-Ws;M=ceil<6.2*pi/tr_width>;n=0:1:M-1;Wc=<Ws+Wp>/2;hd=ideal_lp<pi,M>-ideal_lp<Wc,M>;w_ham=<hanning<M>>';h=hd.*w_ham;[db,mag,pha,w]=freqz_m2<h,[1]>;delta_w=2*pi/1000;Ap=-<min<db<Wp/delta_w+1:1:501>>>As=-round<max<db<1:1:Ws/delta_w+1>>>subplot<221>stem<n,hd>;title<'IdealImpulseRresponse'>axis<[0M-1-0.40.5]>;xlabel<'n'>;ylabel<'hd<n>'>subplot<222>stem<n,w_ham>;title<'HammingWindow'>axis<[0M-101.1]>;xlabel<'n'>;ylabel<'w<n>'>subplot<223>stem<n,h>;title<'ActualImpuseResponse'>axis<[0M-1-0.40.5]>;xlabel<'n'>;ylabel<'h<n>'>subplot<224>plot<w/pi,db>;title<'MagnitudeResponseindb'>;gridaxis<[01-10010]>;xlabel<'frequencein\piunit'>;ylabel<'decibels'>;clearallfigureWp=0.6*pi;Ws=0.4*pi;tr_width=Wp-Ws;M=ceil<6.2*pi/tr_width>n=0:1:M-1;Wc=<Ws+Wp>/2;hd=ideal_lp<pi,M>-ideal_lp<Wc,M>;w_ham=<hanning<M>>;h=hd.*rot90<w_ham>;[db,mag,pha,w]=freqz_m2<h,[1]>;delta_w=2*pi/1000;Ap=-<min<db<Wp/delta_w+1:1:501>>>As=-round<max<db<1:1:Ws/delta_w+1>>>figuresubplot<221>stem<n,hd>;title<'IdealImpulseRresponse'>axis<[0M-1-0.40.5]>;xlabel<'n'>;ylabel<'hd<n>'>subplot<222>stem<n,w_ham>;title<'HammingWindow'>axis<[0M-101.1]>;xlabel<'n'>;ylabel<'w<n>'>subplot<223>stem<n,h>;title<'ActualImpuseResponse'>axis<[0M-1-0.40.5]>;xlabel<'n'>;ylabel<'h<n>'>subplot<224>plot<w/pi,db>;title<'MagnitudeResponseindb'>;gridaxis<[01-10010]>;xlabel<'frequencein\piunit'>;ylabel<'decibels'>;%ó?Hamming′°oˉêyéè??FIRêy×???2¨?÷figurewp=0.2*pi;ws=0.3*piN=61n=[0:1:N-1]wc=<ws+wp>/2;%àí??μíí¨??2¨?÷hd=ideal_lp<wc,N>;%àí??μíí¨μ?3??¤?ìó|w_ham=<hamming<N>>';h=hd.*w_ham;%FIR??2¨?÷3??¤?ìó|[db,mag,pha,grd,w]=freqz_m<h,[1]>;delta_w=2*pi/1000;Rp=-<min<db<1:1:wp/delta_w+1>>>%êμ?êμ?í¨′??￥??As=-round<max<db<ws/delta_w+1:1:501>>>%êμ?êμ?×?D?×è′??￥??subplot<221>;stem<n,hd>;title<'àí??3??¤?ìó|'>axis<[0N-1-0.10.3]>;xlabel<'n'>;ylabel<'hd<n>'>subplot<222>;stem<n,w_ham>;title<'hamming′°'>axis<[0N-101.1]>;xlabel<'n'>;ylabel<'w<n>'>;subplot<223>;stem<n,h>;title<'êμ?ê3??¤?ìó|'>axis<[0N-1-0.10.3]>;xlabel<'n'>;ylabel<'h<n>'>subplot<224>;plot<w/pi,db>;axis<[00.8-1000]>;xlabel<'ò?PI?aμ￥??μ??μ?ê'>;ylabel<'??êy·ù?è/db'>;clearallfigure%ó?Kaiser′°oˉêyéè??FIRêy×???2¨?÷wp=0.2*pi;ws=0.3*pi;As=50tr_width=ws-wpN=ceil<<As-7.95>/<14.36*tr_width/<2*pi>>+1>+1n=[0:1:N-1]beta=0.1102*<As-8.7>wc=<wp+ws>/2%àí??μíí¨μ????1?μ?êhd=ideal_lp<wc,N>w_kai=<kaiser<N,beta>>'h=hd.*w_kai[db,mag,pha,grd,w]=freqz_m<h,[1]>delta_w=2*pi/1000Rp=-<min<db<1:1:wp/delta_w+1>>>%?êμ?êμ?í¨′??￥??As=-round<max<db<ws/delta_w+1:1:501>>>%êμ?êμ?×?D?×è′??￥??subplot<211>;plot<w/pi,db>;title<'?-é-′°·ù?è?ìó|<dB>'>;gridaxis<[00.5-1000]>ylabel<'??êy·ù?è/db'>;xlabel<'ò?/pi?aμ￥??μ??μ?ê'>subplot<212>;plot<w/pi,pha>;title<'?à???ìó|'>;gridaxis<[00.5-44]>ylabel<'?à??'>;xlabel<'ò?/pi?aμ￥??μ??μ?ê'>figureh1=[-4,1,-1,-2,5,6,5,-2,-1,1,-4];M=length<h1>;n=0:M-1;[A,w,type,tao]=amplres<h1>;typesubplot<2,1,1>,stem<n,h1>;title<'3??¤?ìó|h1'>;ylabel<'h<n>'>;xlabel<'n'>;subplot<2,1,2>,plot<w/pi,A>;ylabel<'A'>;xlabel<'\pi'>;title<'?·ù?μ?ìó|'>;figurerz=roots<h1>fori=1:8r<i>=1/rz<i>;endr'zplane<h1,1>;title<'h1á???μ?í?'>;clearallfigureh2=[-4,1,-1,-2,5,6,6,5,-2,-1,1,-4];M=length<h2>;n=0:M-1;[A,w,type,tao]=amplres<h2>;typesubplot<2,1,1>,stem<n,h2>;title<'3??¤?ìó|h2'>;ylabel<'h<n>'>;xlabel<'n'>;subplot<2,1,2>,plot<w/pi,A>;ylabel<'A'>;xlabel<'\pi'>;title<'·ù?μ?ìó|'>;figurerz=roots<h2>fori=1:8r<i>=1/rz<i>;endr'zplane<h2,1>;title<'?h2á???μ?í?'>;clearallfigureh3=[-4,1,-1,-2,5,0,-5,2,1,-1,4];M=length<h3>;n=0:M-1;[A,w,type,tao]=amplres<h3>;typesubplot<2,1,1>,stem<n,h3>;title<'3??¤?ìó|h3'>;ylabel<'h<n>'>;xlabel<'n'>;subplot<2,1,2>,plot<w/pi,A>;ylabel<'A'>;xlabel<'\pi'>;title<'·ù?μ?ìó|?'>;figurerz=roots<h3>fori=1:8r<i>=1/rz<i>;endr'zplane<h3,1>;title<'h3á???μ?í?'>;clearallfigureh4=[-4,1,-1,-2,5,6,-6,-5,2,1,-1,4];M=length<h4>;n=0:M-1;[A,w,type,tao]=amplres<h4>;typesubplot<2,1,1>,stem<n,h4>;title<'3??¤?ìó|h4'>;ylabel<'h<n>'>;xlabel<'n'>;subplot<2,1,2>,plot<w/pi,A>;ylabel<'A'>;xlabel<'\pi'>;title<'?·ù?μ?ìó|?'>;figurerz=roots<h4>fori=1: