信号处理实验五报告

1、实验五 谱分析一、 实验原理 信号是无限长的，而在进行信号处理时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”看无限长的信倍号，或者从分析的角度是无限长的信号乘以有限长的窗函数，由傅里叶变换性质可知如果是频宽有限信号，而是频宽无限函数，截断后的信号也必是频宽无限信号，从而产生所谓的频谱泄漏。频谱泄漏是不可避免的，但要尽量减小，因此设计了不同的窗函数满足不同用途的要求。从能量的角度，频谱泄漏也是能量泄漏，因为加窗后，使原来的信号集中在窄频带内的能量分散到无限的频宽范围。MATLAB信号处理工具箱提供了8种窗函数：(1) 函数boxcar()用于产

2、生矩形窗，调用格式：w=boxcar(N)其中，N为窗长度，w为返回的窗函数序列。矩形窗的表达式为(2) 函数Hanning()用于产生汉宁窗，调用格式：w=hanning(N)Hanning窗表达式为(3) 函数Hamming()用于产生汉明窗，调用格式为w=hamming(N)汉明窗的表达式为(4) 函数bartlett()用于产生巴特利特窗，调用格式为w=bartlett(N)巴特利特窗的表达式为 (5) 函数blackman()用于产生布莱克曼窗，调用格式w=blackman(N)布莱克曼窗表达式为(6) 函数triang()用来产生triang窗，调用格式w=triang(N)tri

3、ang窗类似于bartlett窗，triang窗两端不为0，而bartlett窗两端为0。(7) 函数kaiser()用于产生kaiser窗，调用格式w=kaiser(N,beta) 其中，beta是kaiser窗的参数，影响窗旁瓣幅值的衰减率。kaiser窗表达式式中，是第一类零阶贝塞尔函数，是一个可自由选择的参数，它可以同时调整主瓣宽度与旁瓣电平，越大，则窗越窄，而频谱的旁瓣越小，但主瓣宽度也相应增加。因而改变值就可对主瓣宽度与旁辩衰减进行选择。(8) 函数chebwin()用于产生切比雪夫窗，调用格式w=chebwin(N,r)其中，r是窗口的旁瓣幅值在主瓣以下的分贝数。切比雪夫窗的特点

4、是主瓣的宽度最小，而旁瓣都是等高的且高度可调整。各种窗函数的幅频响应都存在明显的主瓣和旁瓣，主瓣频宽印旁瓣的幅恒定减持性决定f窗函数的应用。不同窗函数在这两方面的特点是不相同的。如blcakman窗具有最宽的主瓣，而chebyshev窗具有最窄的主瓣等。主旁瓣的频宽还与窗长度N有关。增加窗长度N将缩小窗函数主瓣宽度，但不能减小旁瓣幅值衰减相对值(分贝数)，这个值是由窗函数决定的。二、 实验内容1、 用MATLAB编程绘制各种窗函数的形状。 【程序】 16 / 16%-文件exp35_1.m-%绘制各种窗函数clear all;close all;%(1)boxcar产生矩形窗% MATLAB

5、推荐用 RECTWIN 代替 BOXCAR.N1 = 10;n1 = 0:N1-1;w1 = rectwin(N1);hf1 = figure;subplot(2,2,1);stem(n1,w1);title(矩形窗);axis(-5 15 0 1.5);%(2)hanning()产生汉宁窗N2 = 50;n2 = 0:N2-1;w2 = hanning(N2);subplot(2,2,2);stem(n2,w2);title(汉宁窗);axis(-1 50 0 1.5);%(3)hamming()产生汉明窗N3 = 50;n3 = 0:N3-1;w3 = hamming(N3);subplo

6、t(2,2,3);stem(n3,w3);title(汉明窗);axis(-1 50 0 1.5);%(4)bartlett()产生巴特利特窗N4 = 50;n4 = 0:N4-1;w4 = bartlett(N4);subplot(2,2,4);stem(n4,w4);title(巴特利特窗);axis(-1 50 0 1.5);saveas(hf1,exp35.1(1).fig) %(5)blackman产生布莱克曼窗N5 = 50;n5 = 0:N5-1;w5 = blackman(N5);hf2 = figure;subplot(2,2,1);stem(n5,w5);title(布莱克

7、曼窗);axis(0 50 0 1.5);%(6)triang()产生triang窗N6 = 50;n6 = 0:N6-1;w6 = triang(N6);subplot(2,2,2);stem(n6,w6);title(triang窗);axis(0 50 0 1.5);%(7)kaiser()产生kaiser窗N7 = 50;n7 = 0:N7-1;w7 = kaiser(N7);subplot(2,2,3);stem(n7,w7);title(kaiser窗);axis(0 50 0 1.5);%(8)chebwin()产生切比雪夫窗N8 = 50;n8 = 0:N8-1;w8 = ch

8、ebwin(N8);subplot(2,2,4);stem(n8,w8);title(切比雪夫窗);axis(0 50 0 1.5);saveas(hf2,exp35.1(2).fig)【结果及分析】图1.1 窗函数绘制结果（1）图1.2 窗函数绘制结果（2）2、用MATLAB绘制各种窗函数的幅频响应。【程序】%-文件exp35_2.m-clear all;close all;clc;hf1 = figure;%矩形窗b = fir1(50,0.5,rectwin(51);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,1);hAx,hLine1

9、,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(矩形窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%汉宁窗b = fir1(50,0.5,hanning(51);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,2);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(汉宁窗幅频响应);yla

10、bel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%汉明窗b = fir1(50,0.5,hamming(51);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,3);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(汉明窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%巴特利特窗b = fir1(50,0.5,bartlett(51);hd =

11、 dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,4);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(巴特利特窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);hf2=figure;%布莱克曼窗b = fir1(50,0.5,blackman(51);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,1);hAx,hLine1,hLine2=p

12、lotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(布莱克曼窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%triang窗b = fir1(50,0.5,triang(51);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,2);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(triang窗幅频响应);yla

13、bel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%kaiser窗b = fir1(50,0.5,kaiser(51);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,3);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(kaiser窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%切比雪夫窗b = fir1(50,0.5,chebwin(51

14、);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,4);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(切比雪夫窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%保存结果saveas(hf1,exp35.2(1).fig);saveas(hf2,exp35.2(2).fig);【结果及分析】分别绘制8种窗的幅频响应结果如图2.1所示。图2.1（a）图2.1（b）3、 绘制矩形窗

15、的幅频响应，窗长度分别为：N=10，N=20,N=50,N=100。【程序】%-文件exp35_3.m-clear all;close all;clc;hf = figure;%N=10b = fir1(9,0.5,rectwin(10);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,1);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(N=10矩形窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(

16、2),Phase);%N=20b = fir1(19,0.5,rectwin(20);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,2);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(N=20矩形窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%N=50b = fir1(49,0.5,rectwin(50);hd = dfilt.dffir(b);h,w = freqz(hd

17、);subplot(2,2,3);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMALIZED FREQUENCY);title(N=50矩形窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%N=100b = fir1(99,0.5,rectwin(100);hd = dfilt.dffir(b);h,w = freqz(hd);subplot(2,2,4);hAx,hLine1,hLine2=plotyy(w,abs(h),w,angle(h);xlabel(NORMAL

18、IZED FREQUENCY);title(N=100矩形窗幅频响应);ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%保存结果saveas(hf,exp35.3.fig)【结果及分析】绘制N=10,N=20,N=50,N=100,时矩形窗的幅频响应如图3.1所示。图3.1 矩形窗的幅频响应4、已知周期信号 其中f=25/16Hz,若截断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的窗函数提取的x(t)的频谱。(1) 矩形窗；(2)汉宁窗；(3)汉明窗；(4)巴特利特窗；(5)布莱克曼窗；(6)triang窗；(7)Kaiser窗

19、；(8)切比雪夫窗。【程序】%-文件exp35_4.m-clear all;close all;clc;f = 25/16;fs = 12;Tp = 0.64*10;ma1 = 0.9; %截断倍数ma2 = 1.1;%信号采样N1 = ma1*Tp*fs; N1 = round(N1); %采样点数N2 = ma2*Tp*fs; N2 = round(N2); n1 = 0:N1-1;n2 = 0:N2-1;xa1=0.75+3.4*cos(2*pi*f*n1/fs)+2.7*cos(4*pi*f*n1/fs)+1.5*sin(3.5*pi*f*n1/fs)+2.5*sin(7*pi*f*n

20、1/fs);xa2=0.75+3.4*cos(2*pi*f*n2/fs)+2.7*cos(4*pi*f*n2/fs)+1.5*sin(3.5*pi*f*n2/fs)+2.5*sin(7*pi*f*n2/fs);%矩形窗win1 = rectwin(N1);win2 = rectwin(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0

21、,1,NFFT);%函数采样hf1 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(矩形窗0.9Tp截取幅度谱);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(矩形窗0.9Tp截取相位谱);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMA

22、LIZED FREQUENCY);title(矩形窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(矩形窗1.1Tp截取相位谱);ylabel(Phase);%汉宁窗win1 = hanning(N1);win2 = hanning(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,

23、NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函数采样hf2 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(汉宁窗0.9Tp截取幅度谱);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(汉宁窗0.9Tp截取相位谱);ylabel(Phase);%

24、1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(汉宁窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(汉宁窗1.1Tp截取相位谱);ylabel(Phase);%汉明窗win1 = hamming(N1);win2 = hamming(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FF

25、T点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函数采样hf3 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(汉明窗0.9Tp截取幅度谱);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZE

26、D FREQUENCY);title(汉明窗0.9Tp截取相位谱);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(汉明窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(汉明窗1.1Tp截取相位谱);ylabel(Phase);%巴特利特窗win1 = bartlett(N1);win2 = bartlett(N2);%截

27、取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函数采样hf4 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(巴特利特窗0.9Tp截取幅度谱);ylabel(Magnitu

28、de );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(巴特利特窗0.9Tp截取相位谱);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(巴特利特窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(巴特利特窗1.1Tp截取相位谱);y

29、label(Phase);%布莱克曼窗win1 = blackman(N1);win2 = blackman(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函数采样hf5 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabe

30、l(NORMALIZED FREQUENCY);title(布莱克曼窗0.9Tp截取幅度谱);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(布莱克曼窗0.9Tp截取相位谱);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(布莱克曼窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,ang

31、le(XW2);xlabel(NORMALIZED FREQUENCY);title(布莱克曼窗1.1Tp截取相位谱);ylabel(Phase);%triang窗win1 = triang(N1);win2 = triang(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函数采样hf6 = figure;%0

32、.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(triang窗0.9Tp截取幅度谱);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(triang窗0.9Tp截取相位谱);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);titl

33、e(triang窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(triang窗1.1Tp截取相位谱);ylabel(Phase);%kaiser窗win1 = kaiser(N1);win2 = kaiser(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT点数XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 =

34、 fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函数采样hf7 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(kaiser窗0.9Tp截取幅度谱);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(kaiser窗0.9Tp截取相位谱);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(kaiser窗1.1Tp截取幅度谱);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xla