实验五谱分析一.实验原理信号是无限长的，而在进行信号处理是只能采用有限长信号，所以需要将信号“截断”。

在信号处理中，“截断”被看成是用一个有限长的“窗口”看无限长的信号，或者从分析的角度是无限长的信号乘以有限长的窗函数。

二.实验内容1、用matlab编程绘制各种窗函数的形状。

2、用matlab编程绘制各种窗函数的幅频响应。

矩形窗N=20;n=0:(N-1);w=boxcar(N);subplot(211);stem(n,w);title('形状');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('幅频响应');02468101214161820-0.5-0.4-0.3-0.2-0.100.10.20.30.40.505101520矩形窗幅频响应汉宁窗N=20;n=0:(N-1);w=hanning(N);subplot(211);stem(n,w);title('形状');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('幅频响应');02468101214161820-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5051015汉宁窗幅频响应汉明窗N=20;n=0:(N-1);w=hamming(N);subplot(211);stem(n,w);title('形状');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('幅频响应');02468101214161820-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5051015汉明窗幅频响应巴特利特窗N=20;n=0:(N-1);w=bartlett(N);subplot(211);stem(n,w);title('形状');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('幅频响应');巴特利特窗形状-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510巴特利特窗幅频响应布莱克曼窗N=20;n=0:(N-1);w=blackman(N);subplot(211);stem(n,w);title('形状');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('幅频响应');-0.5-0.4-0.3-0.2-0.100.10.20.30.40.502468布莱克曼窗幅频响应Triang 窗N=20;n=0:(N-1);w=triang(N);subplot(211);stem(n,w);title('形状');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('幅频响应');02468101214161820triang 窗形状-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510triang 窗幅频响应Kaiser 窗N=20;n=0:(N-1);w=kaiser(N);subplot(211);stem(n,w);title('kaiser´°ÐÎ×´');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('kaiser´°·ùƵÏìÓ¦');02468101214161820-0.5-0.4-0.3-0.2-0.100.10.20.30.40.505101520kaiser 窗幅频响应切比雪夫窗N=20;n=0:(N-1);w=chebwin(N);subplot(211);stem(n,w);title('Æõ±ÈÑ©·ò´°ÐÎ×´');[H,W]=dtft(w,1024);subplot(212);plot(W/2/pi,abs(H));title('Æõ±ÈÑ©·ò´°·ùƵÏìÓ¦');-0.5-0.4-0.3-0.2-0.100.10.20.30.40.502468契比雪夫窗幅频响应3、绘制矩形窗的幅频响应，窗长度分别为：10.20,50,100.N=10时N=10;n=0:(N-1);w=boxcar(N);[H,W]=dtft(w,1024);plot(W/2/pi,abs(H));title('¾ØÐδ°·ùƵÏìÓ¦');-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5012345678910矩形窗幅频响应N=20时N=20;n=0:(N-1);w=boxcar(N);[H,W]=dtft(w,1024);plot(W/2/pi,abs(H));title('¾ØÐδ°·ùƵÏìÓ¦');-0.5-0.4-0.3-0.2-0.100.10.20.30.40.502468101214161820矩形窗幅频响应N=50时N=50;n=0:(N-1);w=boxcar(N);[H,W]=dtft(w,1024);plot(W/2/pi,abs(H));title('¾ØÐδ°·ùƵÏìÓ¦');-0.5-0.4-0.3-0.2-0.100.10.20.30.40.505101520253035404550矩形窗幅频响应N=100时N=100;n=0:(N-1);w=boxcar(N);[H,W]=dtft(w,1024);plot(W/2/pi,abs(H));title('¾ØÐδ°·ùƵÏìÓ¦');-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50102030405060708090100矩形窗幅频响应4、已知周期信号，若截取时间长度分别为信号周期的0.9和1.1倍，试绘制和比较采用下面窗函数提取的频谱。

0.9倍矩形窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=boxcar(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*sin(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5051015202530354045汉宁窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=hanning(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510152025汉明窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=hamming(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510152025巴特利特窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=bartlett(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.502468101214161820布莱克曼窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=blackman(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50246810121416Triang 窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=triang(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510152025Kaiser 窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=kaiser(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5051015202530354045切比雪夫窗fs=10;Tp=2.56;f=25/16;N=0.9*fs*Tp n=0:(N-1);w=chebwin(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510151.1倍矩形窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=boxcar(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50102030405060汉宁窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=hanning(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510152025汉明窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=hamming(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.5051015202530巴特利特窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=bartlett(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510152025布莱克曼窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=blackman(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.502468101214161820Triang 窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=triang(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50510152025Kaiser 窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=kaiser(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50102030405060切比雪夫窗fs=10;Tp=2.56;f=25/16;N=1.1*fs*Tp n=0:(N-1);w=chebwin(N)t=n/fs;x=0.75+3.4*cos(2*pi*f*t)+2.7*cos(4*pi*f*t)+1.5*sin(3.5*pi*f*t)+2.5*s in(7*pi*f*t);y=w.*x';[H,W]=dtft(y,1000);plot(W/2/pi,abs(H));-0.5-0.4-0.3-0.2-0.100.10.20.30.40.524681012141618。