武汉理工大学基于矩形窗、三角窗、海明窗、汉宁窗、布拉克曼窗的FIR数字滤波器设计

基于矩形窗的FIR数字低通滤波器设计参数如下：主程序：%FIR数字低通滤波器设计wp=2*pi*1.75/15;ws=2*pi*3.25/15w=(wp+ws)/2;N=ceil(4*pi/(ws-wp));n=0:1:(N-1);alpha=(N-1)/2;m=n-alpha+eps;hd=sin(w*m)./(pi*m);%得到抱负低通滤波器B=boxcar(N);h=hd.*(B)”;%FIR数字滤波器[H,w]=freqz(h,[1],1024);%求其频率响应db=20*log10(abs(H)+eps);%得到幅值pha=angle(H);%得到相位figure(1);subplot(2,2,1);axis([0,N-1,-0.1,0.35]);实际低通滤波器的text((0.3*N),0.275,string);subplot(2,2,2);axis([0,1,-100,5]);grid;subplot(2,2,3);plot(w,pha);holdon;”””axis([0,3.2,-4,4]);subplot(2,2,4);plot(w,abs(H));””频率”axis([0,3.15,0,1.5]);text(0.9,1.3,string);基于矩形窗的带通滤波器的设计参数如下：子程序：functionhd=ideal_bs(Wcl,Wch,N)alpha=(N-1)/2;n=0:1:N-1;m=n-alpha+eps;hd=[sin(Wch*m)-sin(Wcl*m)]./(pi*m);functionhd=ideal_bs(Wcl,Wch,N)alpha=(N-1)/2;n=0:1:N-1;m=n-alpha+eps;hd=[sin(Wch*m)-sin(Wcl*m)]./(pi*m);主程序：clearall;Wph=2*pi*4.75/15;Wpl=2*pi*2.5/15;Wsl=2*pi/15;Wsh=2*pi*6.25/15;tr_width=min((Wpl-Wsl),(Wsh-Wph)); %过渡带宽度N=ceil(4*pi/tr_width); %滤波器长度n=0:1:N-1;Wcl=(Wsl+Wpl)/2; %抱负滤波器的截止频率Wch=(Wsh+Wph)/2;hd=ideal_bs(Wcl,Wch,N); %抱负滤波器的单位冲击响应w_ham=(boxcar(N))”;string=[”矩形窗”,”N=”,num2str(N)];h=hd.*w_ham; %截取取得实际的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1]); %计算实际滤波器的幅度响应subplot(3,2,1);stem(n,hd);title(”抱负脉冲响应hd(n)”)axis([-1,N,-0.5,0.8]);xlabel(”n”);ylabel(”hd(n)”);subplot(3,2,2);stem(n,w_ham);axis([-1,N,0,1.1]);xlabel(”n”);ylabel(”w(n)”);text(1.5,1.3,string);subplot(3,2,3);stem(n,h);title(”实际脉冲响应h(n)”);axis([0,N,-1.4,1.4]);xlabel(”n”);ylabel(”h(n)”);subplot(3,2,4);plot(w,pha);title(”相频特性”);axis([0,3.15,-4,4]);xlabel(”频率〔rad〕”);ylabel(”相位〔?〕”);subplot(3,2,5);plot(w/pi,db);title(”幅度特性〔dB〕”);axis([0,1,-80,10]);xlabel(”频率〔pi〕”);ylabel(”分贝数”);subplot(3,2,6);plot(w,mag);title(”频率特性”)axis([0,3.15,0,1.5]);xlabel(”频率〔rad〕”);ylabel(”幅值”);fs=15000t=(0:100)/fsx=sin(2*pi*t*750)+sin(2*pi*t*5000)+sin(2*pi*t*6100)q=filter(h,1,x)[a,f1]=freqz(x)f1=f1/pi*fs/2[b,f2]=freqz(q)f2=f2/pi*fs/2figure(2)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”)基于矩形窗的FIR数字带阻滤波器设计参数：主程序：clearall;Wph=2*pi*6.25/15;Wpl=2*pi/15;Wsl=2*pi*2.5/15;Wsh=2*pi*4.75/15;tr_width=min((Wsl-Wpl),(Wph-Wsh));%过渡带宽度N=ceil(4*pi/tr_width);%滤波器长度n=0:1:N-1;Wcl=(Wsl+Wpl)/2;%抱负滤波器的截止频率Wch=(Wsh+Wph)/2;hd=ideal_bs(Wcl,Wch,N);%抱负滤波器的单位冲击响应w_ham=(boxcar(N))”;string=[”矩形窗”,”N=”,num2str(N)]h=hd.*w_ham;%截取取得实际的单位脉冲响应[db,mag,pha,w]=freqz_m2(h,[1]);%计算实际滤波器的幅度响应delta_w=2*pi/1000;subplot(3,2,1);stem(n,hd);title(hd(n)”)axis([-1,N,-0.5,0.8]);xlabel(”n”);ylabel(”hd(n)”);subplot(3,2,2);stem(n,w_ham);axis([-1,N,0,1.1]);xlabel(”n”);ylabel(”w(n)”);text(1.5,1.3,string);subplot(3,2,3);stem(n,h);title(”实际脉冲响应h(n)”)axis([0,N,-1.4,1.4]);xlabel(”n”);ylabel(”h(n)”);subplot(3,2,4);plot(w,pha);title(”相频特性”)axis([0,3.15,-4,4]);xlabel(”频率〔rad〕”)ylabel(”相位〔Φ〕”)subplot(3,2,5);plot(w/pi,db);title(”幅度特性〔dB〕”)axis([0,1,-80,10]);xlabel(”频率〔pi〕”)ylabel(”分贝数”)subplot(3,2,6);plot(w,mag);title(”频率特性”)axis([0,3,0,2]);xlabel(”频率〔rad〕”)ylabel(”幅值”)fs=15000;t=(0:100)/fs;x=sin(2*pi*t*750)+sin(2*pi*t*3000)+sin(2*pi*t*6100);q=filter(h,1,x);[a,f1]=freqz(x);f1=f1/pi*fs/2;[b,f2]=freqz(q);f2=f2/pi*fs/2;figure(2);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”)；1：functionhd=ideal_bs(Wcl,Wch,m);alpha=(m-1)/2;n=[0:1:(m-1)];m=n-alpha+eps;hd=[sin(m*pi)+sin(Wcl*m)-sin(Wch*m)]./(pi*m)调用程序2：function[db,mag,pha,w]=freqz_m2(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);基于三角窗的FIR数字高通滤波器设计参数：子程序：functionhd=ideal_hp1(Wc,N)alpha=(N-1)/2;n=0:1:N-1;m=n-alpha+eps;%hd=[sin(pi*m)-sin(Wc*m)]/(pi*m);hd=[sin(pi*m)-sin(Wc*m)]./(pi*m);function[db,mag,pha,w]=freqz_m2(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);主程序：clearall;Ws=6.5/15*piWp=3.5/15*pitr_width=Ws-Wp;%过渡带宽度n=0:1:N-1;Wc=(Ws+Wp)/2;%抱负滤波器的截止频率hd=ideal_hp1(Wc,N);%抱负滤波器的单位冲击响应w_ham=(triang(N))”;string=[”三角窗”,”N=”,num2str(N)];h=hd.*w_ham;%截取得到的实际的单位脉冲响应delta_w=2*pi/1000;Ap=-(min(db(Ws/delta_w+1:1:501)));%实际通带波浪hd(n)”);axis([0,N-1,-0.5,0.5]);xlabel(”n”);ylabel(”hd(n)”);subplot(3,2,2);stem(n,w_ham);axis([0,N-1,0,1.1]);xlabel(”n”);ylabel(”w(n)”);text(1.5,1.3,string);subplot(3,2,3);stem(n,h);title(”实际脉冲响应hd(n)”);axis([0,N,-1.4,1.4]);xlabel(”n”);ylabel(”hd(n)”);subplot(3,2,4);plot(w,pha);title(”想频特性”);axis([0,3.15,-4,4]);xlabel(”频率(pi)”);ylabel(”相位(o)”);subplot(3,2,5);plot(w/pi,db);title(”幅度特性(dB)”);(pi)”);ylabel(”(分贝数)”);subplot(3,2,6);plot(w,mag);title(”频率特性”);(rad)”);ylabel(”幅值”);fs=12023;t=(0:100)/fs;x=sin(2*pi*t*750)+sin(2*pi*t*1500)+sin(2*pi*t*3000);q=filter(h,1,x);[a,f1]=freqz(x);f1=f1/pi*fs/2;[b,f2]=freqz(q);f2=f2/pi*fs/2;figure(2);subplot(2,1,1);plot(f1,abs(a));title(”输入波形频谱图”);”);ylabel(”幅度”)subplot(2,1,2);plot(f2,abs(b));