北理工数字信号处理实验4窗函数法设计FIR数字滤波器

实验4窗函数法设计FIR数字滤波器一、实验目的掌握窗函数法和频率取样法设计FIR数字滤波器的原理及具体方法二、实验设备与环境计算机、MATLAB软件环境三、实验理论基础四、实验内容1、设计一个数字低通FIR滤波器，其技术指标如下0.2,0.250.3,50ppstsRdBAdB分别采用矩形窗、汉宁窗、海明窗、布莱克曼窗、凯瑟窗设计该滤波器。结合实验结果，分别讨论采用上述方法设计的数字滤波器是否都能满足给定指标要求。解：①矩形窗wp=0.2*pi;wst=0.3*pi;tr_width=wst-wp;N=ceil(1.8*pi/tr_width)+1;n=0:(N-1);wc=(wp+wst)/2;alpha=(N-1)/2;hd=(wc/pi)*sinc((wc/pi)*(n-alpha));w_boxcar=boxcar(N)';h=hd.*w_boxcar;subplot(221);stem(n,hd,'filled');axistight;xlabel('n');ylabel('hd(n)');[Hr,w1]=zerophase(h);subplot(222);plot(w1/pi,Hr);axistight;xlabel('\omega/\pi');ylabel('H(\omega)');subplot(223);stem(n,h,'filled');axistight;xlabel('n');ylabel('h(n)');[H,w]=freqz(h,1);subplot(224);plot(w/pi,20*log10(abs(H)/max(abs(H))));xlabel('\omega/\pi');ylabel('dB');gridon结果：05101500.10.2nhd(n)00.20.40.60.800.51/H()05101500.10.2nh(n)00.51-100-500/dB不满足指标要求②汉宁窗wp=0.2*pi;wst=0.3*pi;tr_width=wst-wp;N=ceil(6.2*pi/tr_width)+1;n=0:(N-1);wc=(wp+wst)/2;alpha=(N-1)/2;hd=(wc/pi)*sinc((wc/pi)*(n-alpha));w_boxcar=hanning(N)';h=hd.*w_boxcar;subplot(221);stem(n,hd,'filled');axistight;xlabel('n');ylabel('hd(n)');[Hr,w1]=zerophase(h);subplot(222);plot(w1/pi,Hr);axistight;xlabel('\omega/\pi');ylabel('H(\omega)');subplot(223);stem(n,h,'filled');axistight;xlabel('n');ylabel('h(n)');[H,w]=freqz(h,1);subplot(224);plot(w/pi,20*log10(abs(H)/max(abs(H))));xlabel('\omega/\pi');ylabel('dB');gridon结果：020406000.10.2nhd(n)00.20.40.60.800.51/H()020406000.050.10.150.2nh(n)00.51-200-150-100-500/dB不满足指标要求③海明窗wp=0.2*pi;wst=0.3*pi;tr_width=wst-wp;N=ceil(6.6*pi/tr_width)+1;n=0:(N-1);wc=(wp+wst)/2;alpha=(N-1)/2;hd=(wc/pi)*sinc((wc/pi)*(n-alpha));w_boxcar=hamming(N)';h=hd.*w_boxcar;subplot(221);stem(n,hd,'filled');axistight;xlabel('n');ylabel('hd(n)');[Hr,w1]=zerophase(h);subplot(222);plot(w1/pi,Hr);axistight;xlabel('\omega/\pi');ylabel('H(\omega)');subplot(223);stem(n,h,'filled');axistight;xlabel('n');ylabel('h(n)');[H,w]=freqz(h,1);subplot(224);plot(w/pi,20*log10(abs(H)/max(abs(H))));xlabel('\omega/\pi');ylabel('dB');gridon结果：020406000.10.2nhd(n)00.20.40.60.800.51/H()020406000.050.10.150.2nh(n)00.51-150-100-500/dB满足指标要求④布莱克曼窗wp=0.2*pi;wst=0.3*pi;tr_width=wst-wp;N=ceil(11*pi/tr_width)+1;n=0:(N-1);wc=(wp+wst)/2;alpha=(N-1)/2;hd=(wc/pi)*sinc((wc/pi)*(n-alpha));w_boxcar=blackman(N)';h=hd.*w_boxcar;subplot(221);stem(n,hd,'filled');axistight;xlabel('n');ylabel('hd(n)');[Hr,w1]=zerophase(h);subplot(222);plot(w1/pi,Hr);axistight;xlabel('\omega/\pi');ylabel('H(\omega)');subplot(223);stem(n,h,'filled');axistight;xlabel('n');ylabel('h(n)');[H,w]=freqz(h,1);subplot(224);plot(w/pi,20*log10(abs(H)/max(abs(H))));xlabel('\omega/\pi');ylabel('dB');gridon结果：05010000.10.2nhd(n)00.20.40.60.800.51/H()05010000.10.2nh(n)00.51-200-150-100-500/dB满足指标要求⑤凯瑟窗wp=0.2*pi;Rp=0.25;wst=0.3*pi;As=50;tr_width=wst-wp;N=ceil((As-7.95)/2.285/tr_width)+1;B=0.1102*(As-8.7);n=0:(N-1);wc=(wp+wst)/2;alpha=(N-1)/2;hd=(wc/pi)*sinc((wc/pi)*(n-alpha));w_kaiser=kaiser(N,B)';h=hd.*w_kaiser;subplot(221);stem(n,hd,'filled');[Hr,wl]=zerophase(h);subplot(222);plot(wl/pi,Hr);subplot(223);stem(n,h,'filled');[H,w]=freqz(h,1);subplot(224);plot(w/pi,20*log10(abs(H)/max(abs(H))));gridon结果：0204060-0.100.10.20.300.51-0.500.511.50204060-0.100.10.20.300.51-150-100-500不满足指标要求2、设计一个数字带通FIR滤波器，其技术指标如下11220.2,600.35,10.65,10.8,60stSppppstSAdBRdBRdBAdB下阻带边缘：下通带边缘：上通带边缘：上阻带边缘：解：代码：wp1=0.35*pi;Rp=1;wp2=0.65*pi;wst1=0.2*pi;As=50;wst2=0.8*pi;tr_width=wp1-wst1;N=ceil(11*pi/tr_width)+1;n=0:(N-1);wc1=(wp1+wst1)/2;wc2=(wp2+wst2)/2;alpha=(N-1)/2;hd=(wc2/pi)*sinc((wc2/pi)*(n-alpha))-(wc1/pi)*sinc((wc1/pi)*(n-alpha));w_blackman=blackman(N)';h=hd.*w_blackman;subplot(221);stem(n,hd,'filled');[Hr,wl]=zerophase(h);subplot(222);plot(wl/pi,Hr);subplot(223);stem(n,h,'filled');[H,w]=freqz(h,1);subplot(224);plot(w/pi,20*log10(abs(H)/max(abs(H))));gridon结果：020406080-0.4-0.200.20.40.600.51-0.500.511.5020406080-0.4-0.200.20.40.600.51-150-100-5003、采用频率取样设计法设计FIR数字低通滤波器，满足以下指标0.2,0.250.3,50ppstsRdBAdB（1）取N=20，过渡带没有样本（2）取N=40，过渡带有一个样本，T=0.39（3）取N=60，过渡带有两个样本，T1=0.5925，T2=0.1099（4）分别讨论采用上述方法设计的数字滤波器是否都能满足给定指标要求解：①N=20;alpha=(N-1)/2;l=0:N-1;wl=(2*pi/N)*l;Hrs=[1,1,1,zeros(1,15),1,1];Hdr=[1,1,0,0];wdl=[0,0.25,0.25,1];k1=0:floor((N-1)/2);k2=floor((N-1)/2)+1:N-1;angH=[-alpha*(2*pi)/N*k1,alpha*(2*pi)/N*(N-k2)];H=Hrs.*exp(j*angH);h=ifft(H,N);w=[0:500]*pi/500;H=freqz(h,1,w);[Hr,wr]=zerophase(h);subplot(221);plot(wdl,Hdr,wl(1:11)/pi,Hrs(1:11),'o');axis([0,1,-0.1,1.1]);xlabel('\omega(\pi)');ylabel('Hr(k)');subplot(222);stem(l,h,'filled');axis([0,N-1,-0.1,0.3]);xlabel('n');ylabel('h(n)');subplot(223);plot(wr/pi,Hr,wl(1:11)/pi,Hrs(1:11),'o');axis([0,1,-0.2,1.2]);xlabel('\omega(\pi)');ylabel('Hr(w)');subplot(224);plot(w/pi,20*log10((abs(H)/max(abs(H)))));axis([0,1,-50,5]);gridon;xlabel('\omega(\pi)');ylabel('dB');00.5100.51()Hr(k)051015-0.100.10.20.3nh(n)00.5100.51()Hr(w)00.51-40-200()dB②N=40;alpha=(N-1)/2;l=0:N-1;wl=(2*pi/N)*l;Hrs=[1,1,1,1,1,0.39,zeros(1,29),0.39,1,1,1,1];Hdr=[1,1,0.39,0,0];wdl=[0,0.2,0.25,0.3,1];k1=0:floor((N-1)/2);k2=f