Matlab实现数字FIR的高通_带通低通带阻滤波器的解析

利用汉宁窗设计Ⅰ型数字高通滤波器clearall;Wp=0.6*pi;Ws=0.4*pi;tr_width=Wp-Ws;%过渡带宽度N=ceil(6.2*pi/tr_width%滤波器长度n=0:1:N-1;Wc=(Ws+Wp/2;%理想低通滤波器的截止频率hd=ideal_hp1(Wc,N;%理想低通滤波器的单位冲激响应w_han=(hanning(N';%汉宁窗h=hd.*w_han;%截取获取实质的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;Ap=-(min(db(Wp/delta_w+1:1:501%实质通带纹波As=-round(max(db(1:1:Ws/delta_w+1%实质阻带纹波subplot(221stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(222stem(n,w_hantitle('汉宁窗w(n'subplot(223stem(n,htitle('实质单位脉冲响应hd(n'subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]clearall;Wp=0.6*pi;Ws=0.4*pi;tr_width=Wp-Ws;%过渡带宽度N=ceil(6.2*pi/tr_width%滤波器长度n=0:1:N-1;Wc=(Ws+Wp/2;%理想低通滤波器的截止频率hd=ideal_hp1(Wc,N;%理想低通滤波器的单位冲激响应w_han=(hanning(N';%汉宁窗h=hd.*w_han;%截取获取实质的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;Ap=-(min(db(Wp/delta_w+1:1:501%实质通带纹波As=-round(max(db(1:1:Ws/delta_w+1%实质阻带纹波subplot(221stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(222stem(n,w_hantitle('汉宁窗w(n'subplot(223stem(n,htitle('实质单位脉冲响应hd(n'subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]基于切比雪夫一致逼近法设计FIR数字低通滤波器clearall;f=[00.60.71];%给定频率轴分点A=[1100];%给定在这些频率分点上理想的幅频响应weigh=[110];%给定在这些频率分点上的加权b=remez(32,f,A,weigh;%设计出切比雪夫最正确一致逼近滤波器[h,w]=freqz(b,1,256,1;h=abs(h;h=20*log10(h;subplot(211stem(b,'.';grid;title('切比雪夫逼近滤波器的抽样值'subplot(212plot(w,h;grid;title('滤波器幅频特点(dB'利用汉宁窗设计Ⅰ型数字带阻滤波器clearall;Wpl=0.2*pi;Wph=0.8*pi;Wsl=0.4*pi;Wsh=0.6*pi;tr_width=min((Wsl-Wpl,(Wph-Wsh;%过渡带宽度N=ceil(6.2*pi/tr_width%滤波器长度n=0:1:N-1;Wcl=(Wsl+Wpl/2;%理想低通滤波器的截止频率Wch=(Wsh+Wph/2;hd=ideal_bs(Wcl,Wch,N;%理想低通滤波器的单位冲激响应w_hann=(hanning(N';%汉宁窗h=hd.*w_hann;%截取获取实质的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;Ap=-(min(db(1:1:Wpl/delta_w+1%实质通带纹波As=-round(max(db(Wsl/delta_w+1:1:Wsh/delta_w+1%实质阻带纹波subplot(221stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(222stem(n,w_hanntitle('汉宁窗w(n'subplot(223stem(n,htitle('实质单位脉冲响应hd(n'subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]利用三角窗设计Ⅲ型数字带通滤波器clearall;Wpl=0.4*pi;Wph=0.6*pi;Wsl=0.2*pi;Wsh=0.8*pi;tr_width=min((Wpl-Wsl,(Wsh-Wph;%过渡带宽度N=ceil(6.1*pi/tr_width%滤波器长度n=0:1:N-1;Wcl=(Wsl+Wpl/2;%理想低通滤波器的截止频率Wch=(Wsh+Wph/2;hd=ideal_bp2(Wcl,Wch,N;%理想低通滤波器的单位冲激响应w_tri=(triang(N';%三角窗h=hd.*w_tri;%截取获取实质的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;Ap=-(min(db(Wpl/delta_w+1:1:Wph/delta_w+1%实质通带纹波As=-round(max(db(Wsh/delta_w+1:1:501%实质阻带纹波subplot(221stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(222stem(n,w_trititle('三角窗w(n'subplot(223stem(n,htitle('实质单位脉冲响应hd(n'subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]利用布拉克曼窗设计Ⅱ型数字带通滤波器clearall;Wpl=0.4*pi;Wph=0.6*pi;Wsl=0.2*pi;Wsh=0.8*pi;tr_width=min((Wpl-Wsl,(Wsh-Wph;%过渡带宽度N=ceil(11*pi/tr_width+1%滤波器长度n=0:1:N-1;Wcl=(Wsl+Wpl/2;%理想低通滤波器的截止频率Wch=(Wsh+Wph/2;hd=ideal_bp1(Wcl,Wch,N;%理想低通滤波器的单位冲激响应w_bman=(blackman(N';%布拉克曼窗h=hd.*w_bman;%截取获取实质的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;Ap=-(min(db(Wpl/delta_w+1:1:Wph/delta_w+1%实质通带纹波As=-round(max(db(Wsh/delta_w+1:1:501%实质阻带纹波subplot(221stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(222stem(n,w_bmantitle('布拉克曼窗w(n'subplot(223stem(n,htitle('实质单位脉冲响应hd(n'subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]利用海明窗设计Ⅱ型数字低通滤波器clearall;Wp=0.2*pi;Ws=0.4*pi;tr_width=Ws-Wp;%过渡带宽度N=ceil(6.6*pi/tr_width+1%滤波器长度n=0:1:N-1;Wc=(Ws+Wp/2;%理想低通滤波器的截止频率hd=ideal_lp1(Wc,N;%理想低通滤波器的单位冲激响应w_ham=(hamming(N';%海明窗h=hd.*w_ham;%截取获取实质的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;Ap=-(min(db(1:1:Wp/delta_w+1%实质通带纹波As=-round(max(db(Ws/delta_w+1:1:501%实质阻带纹波subplot(221stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(222stem(n,w_hamtitle('海明窗w(n'subplot(223stem(n,htitle('实质单位脉冲响应hd(n'subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]%--------------------------------------------------------function[db,mag,pha,w]=freqz_m2(b,a%滤波器的幅值响应(相对、绝对、相位响应%db:相对幅值响应%mag:绝对幅值响应%pha:相位响应%w采样频率;%b系统函数H(z的分子项(对FIR,b=h%a系统函数H(z的分母项(对FIR,a=1[H,w]=freqz(b,a,1000,'whole';H=(H(1:1:501';w=(w(1:1:501';mag=abs(H;%绝对幅值响应db=20*log10((mag+eps/max(mag;%相对幅值响应pha=angle(H;%相位响应利用模拟Butterworth滤波器设计数字低通滤波器%exa4-8_pulseDFforexample4-8usingButterworthanaloglowpassfiltertodesigndigitallowpassfilter%利用模拟Butterworth滤波器设计数字低通滤波器%脉冲响应不变法wp=0.2*pi;ws=0.3*pi;Rp=1;As=15;T=1;%性能指标Rip=10^(-Rp/20;Atn=10^(-As/20;OmgP=wp*T;OmgS=ws*T;[N,OmgC]=buttord(OmgP,OmgS,Rp,As,'s';%采用模拟滤波器的阶数[cs,ds]=butter(N,OmgC,'s';%设计出所需的模拟低通滤波器[b,a]=impinvar(cs,ds,T;%应用脉冲响应不变法进行变换%求得相对、绝对频响及相位、群延迟响应[db,mag,pha,grd,w]=freqz_m(b,a;%下面绘出各条曲线subplot(2,2,1;plot(w/pi,mag;title('幅频特点';xlabel('w(/pi';ylabel('|H(jw|';axis([0,1,0,1.1];set(gca,'XTickMode','manual','XTick',[00.20.30.51];set(gca,'YTickMode','manual','YTick',[0AtnRip1];gridsubplot(2,2,2;plot(w/pi,db;title('幅频特点(dB';xlabel('w(/pi';ylabel('dB';axis([0,1,-40,5];set(gca,'XTickMode','manual','XTick',[00.20.30.51];set(gca,'YTickMode','manual','YTick',[-40-As-Rp0];gridsubplot(2,2,3;plot(w/pi,pha/pi;title('相频特点';xlabel('w(/pi';ylabel('pha(/pi';axis([0,1,-1,1];set(gca,'XTickMode','manual','XTick',[00.20.30.51];gridsubplot(2,2,4;plot(w/pi,grd;title('群延缓';xlabel('w(/pi';ylabel('Sample';axis([0,1,0,12];set(gca,'XTickMode','manual','XTick',[00.20.30.51];gridfunction[db,mag,pha,grd,w]=freqz_m(b,a%滤波器幅值响应(绝对、相对、相位响应及群延缓%Usage:[db,mag,pha,grd,w]=freqz_m(b,a%500点对应[0,pi]%db相对幅值响应;mag绝对幅值响应;pha相位响应;grd群延缓响应%w采样频率;b系统函数H(z的分子项(对FIR,b=h%a系统函数H(z的分母项(对FIR,a=1[H,w]=freqz(b,a,500;%500点的复频响应mag=abs(H;db=20*log10((mag+eps/max(mag;pha=angle(H;grd=grpdelay(b,a,w;基于频域抽样法的FIR数字带阻滤波器设计clearall;N=41;T1=0.598;alpha=(N-1/2;l=0:N-1;wl=(2*pi/N*l;Hrs=[ones(1,6,T1,zeros(1,7,T1,ones(1,11,T1,zeros(1,7,T1,ones(1,6];理%想振幅采样响应Hdr=[1,1,0,0,1,1];wdl=[0,0.3,0.3,0.7,0.7,1];k1=0:floor((N-1/2;k2=floor((N-1/2+1:N-1;angH=[pi/2-alpha*(2*pi/N*(k1+0.5,-pi/2+alpha*(2*pi/N*(N-k2-0.5];%相位拘束条件Hdk=Hrs.*exp(j*angH;%构成Hd(kh1=ifft(Hdk,N;n=0:1:N-1;h=real(h1.*exp(j*pi*n/N;%实质单位冲激响应[db,mag,pha,w]=freqz_m2(h,[1];[Hr,ww,a,L]=hr_type3(h;%实质振幅响应subplot(221plot(wl/pi+1/N,Hrs,'.',wdl,Hdrtitle('频率样本Hd(k:N=41'axis([01-0.11.2]subplot(222stem(l,htitle('实质单位脉冲响应h(n'subplot(223plot(ww/pi,Hr,wl/pi+1/N,Hrs,'.'title('实质振幅响应H(w'axis([01-0.11.2]subplot(224plot(w/pi,dbtitle('幅度响应(dB'axis([01-8010]function[db,mag,pha,w]=freqz_m(b,a;%滤波器的幅值响应(相对、绝对、相位响应%db:相对幅值响应%mag:绝对幅值响应%pha:相位响应%w采样频率;%b系统函数H(z的分子项(对FIR,b=h%a系统函数H(z的分母项(对FIR,a=1[H,w]=freqz(b,a,1000,'whole';H=(H(1:1:501';w=(w(1:1:501';mag=abs(H;db=20*log10((mag+eps/max(mag;pha=angle(H;pha=unwrap(angle(H;function[Hr,w,c,L]=hr_type3(h;%计算所设计的3型滤波器的振幅响应%Hr=振幅响应%b=3型滤波器的系数%L=Hr的阶次%h=3型滤波器的单位冲击响应M=length(h;L=(M-1/2;c=[2*h(L+1:-1:1];n=[0:1:L];w=[0:1:500]'*2*pi/500;Hr=sin(w*n*c';基于频域抽样法的FIR数字带通滤波器设计wsl=0.12*pi;%低阻带边缘wsh=0.82*pi;%高阻带边缘wpl=0.32*pi;%低通带边缘wph=0.62*pi;%高通带边缘delta=(wpl-wsl;%过分带M=ceil(2*pi*3/delta;%抽样点数al=(M-1/2;wl=(2*pi/M;%抽样间隔k=0:M-1;T1=0.12;T2=0.6;%过渡带样本点Hrs=[zeros(1,ceil(0.12*pi/wl+1,T2,T1,ones(1,ceil(0.3*pi/wl,T1,T2,zeros(1,ceil(0.3734*pi/wl,T2,T1,ones(1,ceil(0.3*pi/wl,T1,T2,zeros(1,ceil(0.12*pi/wl+1];wdl=[00.120.320.620.821];k1=0:floor((M-1/2;k2=floor((M-1/2+1:M-1;angH=[-al*(2*pi/M*k1,al*(2*pi/M*(M-k2];H=Hrs.*exp(j*angH;h=real(ifft(H;%傅立叶反变换figure(1;%冲击响应图stem(k,h;title('impulseresponse';xlabel('n';ylabel('h(n';grid;figure(2;%幅频曲线图Hf=abs(H;w=k*wl/pi;plot(w,Hf,'*b-'axis([01-0.11.1];title('amplituderesponse';xlabel('frequencyinpiunits';ylabel('Hr(w';set(gca,'xtickmode','manual','xtick',wdl;set(gca,'ytickmode','manual','ytick',[00.120.61];grid;figure(3;fs=15000;[c,f3]=freqz(h,1;f3=f3/pi*fs/2;plot(f3,20*log10(abs(c;title('频谱特点';xlabel('频率/HZ';ylabel('衰减/dB';grid;t=(0:100/fs;x=sin(2*pi*t*700+sin(2*pi*t*3200+sin(2*pi*t*6200;q=filter(h,1,x;[a,f1]=freqz(x;f1=f1/pi*fs/2;[b,f2]=freqz(q;f2=f2/pi*fs/2;figure(4;subplot(2,1,1;plot(f1,abs(a;title('输入波形频谱图';xlabel('频率';ylabel('幅度'subplot(2,1,2;plot(f2,abs(b;title('输出波形频谱图';xlabel('频率';ylabel('幅度'基于汉宁窗的FIR数字高通滤波器设计functions2Fs=15000;t=(0:100/Fs;x=sin(2*pi*500*t+sin(2*pi*3000*tsubplot(245;stem(x;title('原始信号';axis([0,100,-2,2];Ws=7*pi/30;Wp=13*pi/30;tr_wid=Wp-Ws;%过渡带宽度N=ceil(11*pi/tr_wid%滤波器长度n=0:1:N-1;Wc=(Ws+Wp/2;%理想高通滤波器的截止频率hd=ideal_hp1(Wc,N;%理想高通滤波器的单位冲激响应w_bla=(blackman(N';%布拉克曼h=hd.*w_bla;%截取获取实质的单位脉冲响应[db,mag,pha,grd,w]=freqz_m(h,[1];%计算实质滤波器的幅度响应delta_w=2*pi/1000;As=-round(max(db(1:1:Ws/delta_w+1%实质阻带纹波,round是取整函数y=filter(h,1,xsubplot(246plot(ytitle('滤波后的信号';axis([0,100,-1,1]subplot(241stem(n,hdtitle('理想单位脉冲响应hd(n'subplot(242stem(n,w_blatitle('布拉克满窗w(n'subplot(243stem(n,htitle('实质单位脉冲响应hd(n'subplot(244plot(w/pi,dbtitle('幅度响应(dB'axis([0,1,-100,10]function[db,mag,pha,grd,w]=freqz_m(b,a;[H,w]=freqz(b,a,1000,'whole';H=(H(1:1:501';w=(w(1:1:501';mag=abs(H;db=20*log10((mag+eps/max(mag;pha=angle(H;grd=grpdelay(b,a,w;subplot(247;plot(phatitle('相频响应'functionhd=ideal_hp1(Wc,Nalp=(N-1/2;n=0:1:N-1;m=n-alp+eps;%eps是一个很小很小的数hd=[sin(pi*m-sin(Wc*m]./(pi*m;用双线性法设计巴特沃斯高通数字滤波器clearall;clc;closeallfs=120;T=1/fs;rp=1;rs=30;Wp=0.35*pi;Ws=0.65*pi;%数字滤波器指标wp=2*tan(Wp/2/T;ws=2*tan(Ws/2/T;%预畸变，将数字滤波器的指标变为模拟滤波器的指标[N,w]=buttord(wp,ws,rp,rs,'s';%求滤波器阶数和3dB截止频率[Z,P,K]=buttap(N;%设计模拟低通滤波器[Md,Nd]=zp2tf(Z,P,K;%将零极点形式转换为传输函数形式[M,N]=lp2hp(Md,Nd,w;%对低通滤波器进行频率变换[h,w]=freqs(M,N,512;%模拟滤波器的幅频响应subplot(2,1,1;plot(w,abs(h;grid;xlabel('Hz';ylabel('幅度';title('模拟高通滤波器';[Mh,Nh]=bilinear(M,N,1/T;%对模拟滤波器双线性变换[h1,w1]=freqz(Mh,Nh;%数字滤波器的幅频响应subplot(2,1,2;plot(w1/pi,20*log10(abs(h1;grid;xlabel('幅ω度/(dB';π';ylabel('title('数字高通滤波器';%图-5模拟滤波器与设计的滤波器的单位冲击响应k=0:2000;k2=1:1001;x=10*sin(pi/10*k/fs+5*sin(10*pi*k/fs+3*sin(30*pi*k/fs;figuresubplot(2,1,1X=fft(x*2/2001;y=filter(Mh,Nh,x;plot(k,y;ylim([-55];title('高通数字滤波器输出';Y=fft(y*2/2001;df=fs/2001;ff=(k2-1*df;subplot(2,1,2;plot(ff,abs(X(k2,'r','linewidth',2;holdonplot(ff,abs(Y(k2,'b';title('输入输出频谱比较';grid;