哈工程数字信号处理第五次.doc

实验五 谱分析 一 实验目的 1 研究不同类型的窗函数，研究一些不同的方法来测试窗的性能； 2 专注于有关窄带信号的几个不同的情形。 二 实验原理 信号是无限长的，而在进行信号处理时只能采用有限长信号，所以需要将 窄带信号“截断”。在信号处理中，“截断”被看成是用一个有限长的“窗口”看无限长的信倍号，或者从分析的角度是无限长的信号x(t)乘以有限长的窗函数w(t),由傅立叶变换性质可知：x(t)w(t)=1/2X(jw)W(jw) 如果x(t)是频带有限信号，而w(t)是频带无限函数，截断后的信号也必是频带无限信号，从而产生所谓的频谱泄露。频谱泄露是不可避免的，但是尽量减小，因此设计了不同的窗函数满足不同的要求。从能量的角度，频谱泄露也是能量泄露，因为加窗后，是原来的信号集中在宅频带内的能量分散到无限的频带范围。三 实验内容、程序及结果用MATLAB编程绘制各种窗函数的形状及其幅度响应。w1=boxcar(30);subplot(421)stem(w1)title(juxingchang)xlabel(t);ylabel(w1);w2=hanning(30);subplot(422)stem(w2)title(hanningchuang)xlabel(t);ylabel(w2);w3=hamming(30);subplot(423)stem(w3)title(hanmingchuang);xlabel(t);ylabel(w3);w4=bartlett(30);subplot(424)stem(w4)title(batelitechuang)xlabel(t);ylabel(w4);w5=blackman(30);subplot(425)stem(w5)title(balaikemanchuang)xlabel(t);ylabel(w5);w6=triang(30);subplot(426)stem(w6)title(triang)xlabel(t);ylabel(w6);w7=kaiser(30,60);subplot(427)stem(w7)title(kaiser)xlabel(t);ylabel(w7);w8=chebwin(30,60);subplot(428)stem(w8)title(chebwin)xlabel(t);ylabel(w8);2,各种窗函数的幅频响应 w1=boxcar(30);X,W=dtft(w1,300)subplot(421)plot(W/2/pi,abs(X);title(juxingchuang);xlabel(w);ylabel(|W(jw)|);w2=hanning(30);X,W=dtft(w2,300)subplot(422)plot(W/2/pi,abs(X);title(hanningchuang);xlabel(w);ylabel(|W(jw)|);w3=hamming(30);X,W=dtft(w3,300)subplot(423)plot(W/2/pi,abs(X);title(hanmingchuang);xlabel(w);ylabel(|W(jw)|);w4=bartlett(30);X,W=dtft(w4,300)subplot(424)plot(W/2/pi,abs(X);title(batelite);xlabel(w);ylabel(|W(jw)|);w5=blackman(30);X,W=dtft(w5,300)subplot(425)plot(W/2/pi,abs(X);title(bulaikemanchuang);xlabel(w);ylabel(|W(jw)|);w6=triang(30);X,W=dtft(w6,300)subplot(426)plot(W/2/pi,abs(X);title(triang);xlabel(w);ylabel(|W(jw)|);w7=kaiser(30,60);X,W=dtft(w7,300)subplot(427)plot(W/2/pi,abs(X);title(kaiser);xlabel(w);ylabel(|W(jw)|);w8=chebwin(30,60);X,W=dtft(w8,300)subplot(428)plot(W/2/pi,abs(X);title(chebwin);xlabel(w);ylabel(|W(jw)|);3矩形窗的幅频响应w1=boxcar(10);X,W=dtft(w1,300)subplot(221)plot(W/2/pi,abs(X);title(juxingchuang);xlabel(w);ylabel(|W(jw)|);w2=boxcar(20);X,W=dtft(w2,300)subplot(222)plot(W/2/pi,abs(X);title(juxingchuang);xlabel(w);ylabel(|W(jw)|);w3=boxcar(50);X,W=dtft(w3,300)subplot(223)plot(W/2/pi,abs(X);title(juxingchuang);xlabel(w);ylabel(|W(jw)|);w4=boxcar(100);X,W=dtft(w4,300)subplot(224)plot(W/2/pi,abs(X);title(juxingchuang);xlabel(w);ylabel(|W(jw)|);4.1信号周期的0.9矩形窗和汉宁窗f=25/16;T=2.56;fs=8;N=0.9*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=boxcar(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期0.9的矩形窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期0.9的矩形窗相频);xlabel(f);ylabel(Y1);w2=hanning(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期0.9的汉宁窗幅频);xlabel(f);ylabel(|Y2|);subplot(224),plot(W/2/pi,angle(Y2);title(信号周期0.9的汉宁窗相频);xlabel(f);ylabel(Y2);汉明窗和巴特利特窗f=25/16;T=2.56;fs=8;N=0.9*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=hamming(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期0.9的汉明窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期0.9的汉明窗相频);xlabel(f);ylabel(Y1);w2=bartlett(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期0.9的巴特利特窗幅频);xlabel(f);ylabel(|Y2|);subplot(224),plot(W/2/pi,angle(Y2);title(信号周期0.9的巴特利特窗相频);xlabel(f);ylabel(Y2);布莱克曼窗和Triang窗f=25/16;T=2.56;fs=8;N=0.9*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=blackman(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期0.9的布莱克曼窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期0.9的布莱克曼窗相频);xlabel(f);ylabel(Y1);w2=triang(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期0.9的Triang窗幅频);xlabel(f);ylabel(|Y2|);subplot(224),plot(W/2/pi,angle(Y2);title(信号周期0.9的Triang窗相频);xlabel(f);ylabel(Y2);Kaiser窗和切比雪夫窗f=25/16;T=2.56;fs=8;N=0.9*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=kaiser(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期0.9的Kaiser窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期0.9的Kaiser窗相频);xlabel(f);ylabel(Y1);w2=chebwin(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期0.9的切比雪夫窗幅频);xlabel(f);ylabel(|Y2|);subplot(224),plot(W/2/pi,angle(Y2);title(信号周期0.9的切比雪夫窗相频);xlabel(f);ylabel(Y2);4.2信号周期的1.1矩形窗和汉宁窗f=25/16;T=2.56;fs=8;N=1.1*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=boxcar(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期1.1的矩形窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期1.1的矩形窗相频);xlabel(f);ylabel(Y1);w2=hanning(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期1.1的汉宁窗幅频);xlabel(f);ylabel(|Y2|);subplot(224),plot(W/2/pi,angle(Y2);title(信号周期1.1的汉宁窗相频);xlabel(f);ylabel(Y2);汉明窗和巴特利特窗f=25/16;T=2.56;fs=8;N=1.1*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=hamming(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期1.1的汉明窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期1.1的汉明窗相频);xlabel(f);ylabel(Y1);w2=bartlett(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期1.1的巴特利特窗幅频);xlabel(f);ylabel(|Y2|);subplot(224),plot(W/2/pi,angle(Y2);title(信号周期1.1的巴特利特窗相频);xlabel(f);ylabel(Y2);布莱克曼窗和Triang窗f=25/16;T=2.56;fs=8;N=1.1*T*fs;n=0:(N-1);x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs);w1=blackman(N);y1=x.*w1;Y1,W=dtft(y1,1000);subplot(221),plot(W/2/pi,abs(Y1);title(信号周期1.1的布莱克曼窗幅频);xlabel(f);ylabel(|Y1|);subplot(222),plot(W/2/pi,angle(Y1);title(信号周期1.1的布莱克曼窗相频);xlabel(f);ylabel(Y1);w2=triang(N);y2=x.*w2;Y2,W=dtft(y2,1000);subplot(223),plot(W/2/pi,abs(Y2);title(信号周期1.1的Triang窗幅频);xlabel(f);ylabel(|Y2|);subplo