信號處理實驗五報告

1、實驗五 譜分析一、 實驗原理 信號是無限長的，而在進行信號處理時只能采用有限長信號，所以需要將信號“截斷”。在信號處理中，“截斷”被看成是用一個有限長的“窗口”看無限長的信倍號，或者從分析的角度是無限長的信號乘以有限長的窗函數(shù)，由傅里葉變換性質(zhì)可知如果是頻寬有限信號，而是頻寬無限函數(shù)，截斷后的信號也必是頻寬無限信號，從而產(chǎn)生所謂的頻譜泄漏。頻譜泄漏是不可避免的，但要盡量減小，因此設(shè)計了不同的窗函數(shù)滿足不同用途的要求。從能量的角度，頻譜泄漏也是能量泄漏，因為加窗后，使原來的信號集中在窄頻帶內(nèi)的能量分散到無限的頻寬范圍。MATLAB信號處理工具箱提供了8種窗函數(shù)：(1) 函數(shù)boxcar()用于產(chǎn)

2、生矩形窗，調(diào)用格式：w=boxcar(N)其中，N為窗長度，w為返回的窗函數(shù)序列。矩形窗的表達式為(2) 函數(shù)Hanning()用于產(chǎn)生漢寧窗，調(diào)用格式：w=hanning(N)Hanning窗表達式為(3) 函數(shù)Hamming()用于產(chǎn)生漢明窗，調(diào)用格式為w=hamming(N)漢明窗的表達式為(4) 函數(shù)bartlett()用于產(chǎn)生巴特利特窗，調(diào)用格式為w=bartlett(N)巴特利特窗的表達式為 (5) 函數(shù)blackman()用于產(chǎn)生布萊克曼窗，調(diào)用格式w=blackman(N)布萊克曼窗表達式為(6) 函數(shù)triang()用來產(chǎn)生triang窗，調(diào)用格式w=triang(N)tri

3、ang窗類似于bartlett窗，triang窗兩端不為0，而bartlett窗兩端為0。(7) 函數(shù)kaiser()用于產(chǎn)生kaiser窗，調(diào)用格式w=kaiser(N,beta) 其中，beta是kaiser窗的參數(shù)，影響窗旁瓣幅值的衰減率。kaiser窗表達式式中，是第一類零階貝塞爾函數(shù)，是一個可自由選擇的參數(shù)，它可以同時調(diào)整主瓣寬度與旁瓣電平，越大，則窗越窄，而頻譜的旁瓣越小，但主瓣寬度也相應(yīng)增加。因而改變值就可對主瓣寬度與旁辯衰減進行選擇。(8) 函數(shù)chebwin()用于產(chǎn)生切比雪夫窗，調(diào)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貝數(shù)。切比雪夫窗的特點

4、是主瓣的寬度最小，而旁瓣都是等高的且高度可調(diào)整。各種窗函數(shù)的幅頻響應(yīng)都存在明顯的主瓣和旁瓣，主瓣頻寬印旁瓣的幅恒定減持性決定f窗函數(shù)的應(yīng)用。不同窗函數(shù)在這兩方面的特點是不相同的。如blcakman窗具有最寬的主瓣，而chebyshev窗具有最窄的主瓣等。主旁瓣的頻寬還與窗長度N有關(guān)。增加窗長度N將縮小窗函數(shù)主瓣寬度，但不能減小旁瓣幅值衰減相對值(分貝數(shù))，這個值是由窗函數(shù)決定的。二、 實驗內(nèi)容1、 用MATLAB編程繪制各種窗函數(shù)的形狀。 【程序】 16 / 16%-文件exp35_1.m-%繪制各種窗函數(shù)clear all;close all;%(1)boxcar產(chǎn)生矩形窗% MATLAB

5、推薦用 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()產(chǎn)生漢寧窗N2 = 50;n2 = 0:N2-1;w2 = hanning(N2);subplot(2,2,2);stem(n2,w2);title(漢寧窗);axis(-1 50 0 1.5);%(3)hamming()產(chǎn)生漢明窗N3 = 50;n3 = 0:N3-1;w3 = hamming(N3);subplo

6、t(2,2,3);stem(n3,w3);title(漢明窗);axis(-1 50 0 1.5);%(4)bartlett()產(chǎn)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產(chǎn)生布萊克曼窗N5 = 50;n5 = 0:N5-1;w5 = blackman(N5);hf2 = figure;subplot(2,2,1);stem(n5,w5);title(布萊克

7、曼窗);axis(0 50 0 1.5);%(6)triang()產(chǎn)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()產(chǎn)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()產(chǎn)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)【結(jié)果及分析】圖1.1 窗函數(shù)繪制結(jié)果（1）圖1.2 窗函數(shù)繪制結(jié)果（2）2、用MATLAB繪制各種窗函數(shù)的幅頻響應(yīng)。【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(矩形窗幅頻響應(yīng));ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%漢寧窗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(漢寧窗幅頻響應(yīng));yla

10、bel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%漢明窗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(漢明窗幅頻響應(yīng));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(巴特利特窗幅頻響應(yīng));ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);hf2=figure;%布萊克曼窗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(布萊克曼窗幅頻響應(yīng));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窗幅頻響應(yīng));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窗幅頻響應(yīng));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(切比雪夫窗幅頻響應(yīng));ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%保存結(jié)果saveas(hf1,exp35.2(1).fig);saveas(hf2,exp35.2(2).fig);【結(jié)果及分析】分別繪制8種窗的幅頻響應(yīng)結(jié)果如圖2.1所示。圖2.1（a）圖2.1（b）3、 繪制矩形窗

15、的幅頻響應(yīng)，窗長度分別為：N=10，N=20,N=50,N=100?！境绦颉?-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矩形窗幅頻響應(yīng));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矩形窗幅頻響應(yīng));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矩形窗幅頻響應(yīng));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矩形窗幅頻響應(yīng));ylabel(hAx(1),Magnitude);ylabel(hAx(2),Phase);%保存結(jié)果saveas(hf,exp35.3.fig)【結(jié)果及分析】繪制N=10,N=20,N=50,N=100,時矩形窗的幅頻響應(yīng)如圖3.1所示。圖3.1 矩形窗的幅頻響應(yīng)4、已知周期信號 其中f=25/16Hz,若截斷時間長度分別為信號周期的0.9和1.1倍，試繪制和比較采用下面的窗函數(shù)提取的x(t)的頻譜。(1) 矩形窗；(2)漢寧窗；(3)漢明窗；(4)巴特利特窗；(5)布萊克曼窗；(6)triang窗；(7)Kaiser窗

19、；(8)切比雪夫窗?！境绦颉?-文件exp35_4.m-clear all;close all;clc;f = 25/16;fs = 12;Tp = 0.64*10;ma1 = 0.9; %截斷倍數(shù)ma2 = 1.1;%信號采樣N1 = ma1*Tp*fs; N1 = round(N1); %采樣點數(shù)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點數(shù)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);%函數(shù)采樣hf1 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(矩形窗0.9Tp截取幅度譜);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(矩形窗0.9Tp截取相位譜);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMA

22、LIZED FREQUENCY);title(矩形窗1.1Tp截取幅度譜);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(矩形窗1.1Tp截取相位譜);ylabel(Phase);%漢寧窗win1 = hanning(N1);win2 = hanning(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT點數(shù)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);%函數(shù)采樣hf2 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(漢寧窗0.9Tp截取幅度譜);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(漢寧窗0.9Tp截取相位譜);ylabel(Phase);%

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

25、T點數(shù)XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函數(shù)采樣hf3 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(漢明窗0.9Tp截取幅度譜);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZE

26、D FREQUENCY);title(漢明窗0.9Tp截取相位譜);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(漢明窗1.1Tp截取幅度譜);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(漢明窗1.1Tp截取相位譜);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點數(shù)XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函數(shù)采樣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截取幅度譜);ylabel(Magnitu

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

29、label(Phase);%布萊克曼窗win1 = blackman(N1);win2 = blackman(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT點數(shù)XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函數(shù)采樣hf5 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabe

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

31、le(XW2);xlabel(NORMALIZED FREQUENCY);title(布萊克曼窗1.1Tp截取相位譜);ylabel(Phase);%triang窗win1 = triang(N1);win2 = triang(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT點數(shù)XW1 = fft(xw1,NFFT);W1 = 2*pi*fs*linspace(0,1,NFFT);XW2 = fft(xw2,NFFT);W2 = 2*pi*fs*linspace(0,1,NFFT);%函數(shù)采樣hf6 = figure;%0

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

33、e(triang窗1.1Tp截取幅度譜);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xlabel(NORMALIZED FREQUENCY);title(triang窗1.1Tp截取相位譜);ylabel(Phase);%kaiser窗win1 = kaiser(N1);win2 = kaiser(N2);%截取xw1 = xa1.*win1;xw2 = xa2.*win2;%DFTNFFT = 2048; %FFT點數(shù)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);%函數(shù)采樣hf7 = figure;%0.9Tpsubplot(2,2,1);%plot(W1,abs(XW1);plot(W1,abs(XW1);xlabel(NORMALIZED FREQUENCY);title(kaiser窗0.9Tp截取幅度譜);ylabel(Magnitude );subplot(2,2,3);plot(W1,angle(XW1);xlabel(NORMALIZED FREQUENCY);title(kaiser窗0.9Tp截取相位譜);ylabel(Phase);%1.1Tpsubplot(2,2,2);plot(W2,abs(XW2);xlabel(NORMALIZED FREQUENCY);title(kaiser窗1.1Tp截取幅度譜);ylabel(Magnitude);subplot(2,2,4);plot(W2,angle(XW2);xla