信号谱分析-窗函数

实验三、信号的谱分析五、窗函数windowMATLABhelpwindow可以支持的窗函数类型。help@bartlett -Bartlettwindow.@barthannwin -ModifiedBartlett-Hanningwindow.@blackman -Blackmanwindow.@blackmanharris-Minimum4-termBlackman-Harriswindow.@bohmanwin -Bohmanwindow.@chebwin -Chebyshevwindow.@flattopwin -FlatTopwindow.@gausswin -Gaussianwindow.@hamming -Hammingwindow.@hann -Hannwindow.@kaiser -Kaiserwindow.@nuttallwin -Nuttalldefinedminimum4-termBlackman-Harriswindow.@parzenwin -Parzen(delaValle-Poussin)window.@rectwin -Rectangularwindow.@tukeywin -Tukeywindow.@triang -Triangularwindow.用w产生的各种窗函数（可以设，观察各个窗函数的波形。N=128;w=window(@bartlett,N);plot(1:N,w)bartlett10.90.80.70.60.50.40.30.20.100 20 40 60 80 100 120 140plot(1:N,w1)10.90.80.70.60.50.40.30.2

barthannwin0.100 20 40 60 80 100 120 140w2=window(@blackman,N);plot(1:N,w2)blackman10.90.80.70.60.50.40.30.20.100 20 40 60 80 100 120 140plot(1:N,w3)10.90.80.70.60.50.40.30.2

chebwin0.100 20 40 60 80 100 120 140w4=window(@gausswin,N);plot(1:N,w4)gausswin10.90.80.70.60.50.40.30.20.100 20 40 60 80 100 120 140w5=window(@hamming,N);plot(1:N,w5)hamming10.90.80.70.60.50.40.30.20.100 20 40 60 80 100 120 140计算并分析各个窗函数的谱，观测其谱形状的特点。用wvtool函数观察各窗函数的幅频和相频特性：同上w~w5N=128;w=window(@bartlett,N);w1=window(@barthannwin,N);w2=window(@blackman,N);w3=window(@chebwin,N);w4=window(@gausswin,N);w5=window(@hamming,N);subplot(3,1,1);wvtool(w);ylabel('barlett');subplot(3,1,2);wvtool(w1);ylabel('barthannwin');subplot(3,1,3);wvtool(w2);ylabel('blackman');subplot(6,1,4);wvtool(w3);ylabel('chebwin');subplot(6,1,5);wvtool(w4);ylabel('gausswin');subplot(6,1,6);wvtool(w5);ylabel('hamming');TimedomainTimedomainFrequencydomain401200.8d0l u -200.6d(mA0.4M-400.2-600-8020 4060Samples80100 12000.20.40.60.8NormalizedFrequency( rad/sample)TimedomainTimedomainFrequencydomain401200.80d0.6d(-20mA0.4M-40-600.2-800-10020 4060Samples80100 12000.20.40.60.8NormalizedFrequencyrad/sample)TimedomainTimedomainFrequencydomain1 500.80d0.6d(-50mA 0.40.2M-100-1500-20020 4060Samples80100 12000.20.40.60.8NormalizedFrequencyrad/sample)TimedomainTimedomainFrequencydomain5010.80ddl u -500.6(mA0.4M-1000.20-15020 4060Samples80100 12000.20.40.60.8NormalizedFrequencyrad/sample)TimedomainTimedomainFrequencydomain401200.80d0.6d(-20mA0.4M-40-600.2-800-10020 4060Samples80100 12000.20.40.60.8NormalizedFrequencyrad/sample)TimedomainTimedomainFrequencydomain401200.80d-20l u -400.6d(mA0.4M-60-800.2-1000-12020 4060Samples80100 12000.20.40.60.8NormalizedFrequencyrad/sample)六、关于谱分析的截断效应实验1.N=20;fori=1:Nt(i)=0.01*(i-N/2);w(i)=(i-N/2)*200*pi/N;x(i)=2*sin(4*pi*t(i))+5*cos(6*pi*t(i));endG=fft(g)/100;plot(w(1:N),abs(G(1:N)));xlabel('w');ylabel('G');title('N=20');N=30;fori=1:Nt(i)=0.01*(i-N/2);w(i)=(i-N/2)*200*pi/N;x(i)=2*sin(4*pi*t(i))+5*cos(6*pi*t(i));endX=fft(x)/100;plot(w(1:N),abs(X(1:N)));xlabel('w');ylabel('X');title('N=30');N=50;fori=1:Nt(i)=0.01*(i-N/2);w(i)=(i-N/2)*200*pi/N;x(i)=2*sin(4*pi*t(i))+5*cos(6*pi*t(i));endX=fft(x)/100;plot(w(1:N),abs(X(1:N)));xlabel('w');ylabel('X');title('N=50');N=100;fori=1:Nt(i)=0.01*(i-N/2);w(i)=(i-N/2)*200*pi/N;x(i)=2*sin(4*pi*t(i))+5*cos(6*pi*t(i));endX=fft(x)/100;plot(w(1:N),abs(X(1:N)));xlabel('w');ylabel('X');title('N=100');N=150;fori=1:Nt(i)=0.01*(i-N/2);w(i)=(i-N/2)*200*pi/N;x(i)=2*sin(4*pi*t(i))+5*cos(6*pi*t(i));endX=fft(x)/100;plot(w(1:N),abs(X(1:N)));xlabel('w');ylabel('X');title('N=150');进一步思考，为什么N=100的时候观察不到截断效应？因为N=100时，正好等于其取样频率，所以观察不到截断效应。2.观察各种窗函数对截断效应的改善情况。N=200;fori=1:Nt(i)=0.01*(i-N/2);w(i)=(i-N/2)*200*pi/N;x(i)=2*sin(4*pi*t(i))+5*cos(6*pi*t(i));endwin1=window(@bartlett,N).*x';win2=window(@barthannwin,N).*x';win3=window(@blackman,N).*x';win4=window(@chebwin,N).*x';win5=window(@gausswin,N).*x';win6=window(@hamming,N).*x';G1=fft(x)/100;%G2=fft(win1)/100;%G3=fft(win2)/100;%G4=fft(win3)/100;%G5=fft(win4)/100;%G6=fft(win5)/100;%G7=fft(win6)/100;%plot(w(1:N),abs(G1(1:N)))%title('x(t)');%plot(w(1:N),abs(G2(1:N)))%ylabel('bartlett');%plot(w(1:N),abs(G3(1:N)))%ylabel('barthannwin');plot(w(1:N),abs(G4(1:N)))ylabel('blackman');%plot(w(1:N),abs(G4(1:N)))%ylabel('chebwin');%plot(w(1:N),abs(G4(1:N)))%ylabel('gausswin');%plot(w(1:N),abs(G4(1:N)))%ylabel('hamming');x(t)6543210-400 -300 -200 -100 0 100 200 300 4002.521.5ab10.50-400 -300 -200 -100 0 100 200 300 4002.52n 1.5iwnnahr1ab10.50-400 -300 -200 -100 0 100 200 300 4002.521.5namkab 10.50-400 -300 -200 -100 0 100 200 300 400由图可以看出，加窗函数后，截断效应减弱，图的分辨率变高。七、观察高斯序列的时域和频域特性。1、p=8,q=2,4,8时域分析p=8;q=2;n=0:1:15x=exp(-(n-p).^2/q);stem(x)ylabel('x(n)');xlabel('n');title('p=8,q=2时的时域特性');p=8;q=4;n=0:1:15x=exp(-(n-p).^2/q);stem(x)ylabel('x(n)');xlabel('n');title('p=8,q=4时的时域特性');p=8;q=8;n=0:1:15x=exp(-(n-p).^2/q);stem(x)ylabel('x(n)');xlabel('n');title('p=8,q=4时的时域特性');10.90.80.70.6) x0.40.30.2

p=8,q=2时的时域特性0.100 2 4 6 8n

10 12 14 1610.90.80.70.6) x0.40.30.2

p=8,q=4时的时域特性0.100 2 4 6 8n

10 12 14 1610.90.80.70.6) x0.40.30.2

p=8,q=8时的时域特性0.100 2 4 6 8n

10 12 14 16频域分析clc;clearp=8;q=2;fori=1:100ifi<16x(i)=exp((-(i-p)^2)/q);elsex(i)=0;endendfori=1:80w(i)=(i-40)/10;fork=1:16dtft(i)=dtft(i)+x(k)*exp(-j*(k-1)*w(i));endendsubplot(1,2,1);');subplot(1,2,2);');p=8;q=2幅频特性3 2.5 2

p=8;q=2相频特性T TT0TF 1.5 FT0TDDD1 -10.5 -20 -3-4-2024-4-2024wwclc;clearp=8;q=4;fori=1:100ifi<16x(i)=exp((-(i-p)^2)/q);elsex(i)=0;endendfori=1:80w(i)=(i-40)/10;fork=1:16dtft(i)=dtft(i)+x(k)*exp(-j*(k-1)*w(i));endendsubplot(1,2,1);');subplot(1,2,2);');43.532.52TFTD21.510.50

p=8;q=4幅频特性

p=8;q=4相频特性3210TFTD0-1-2-3-4-2024-4-2024wwclc;clearp=8;q=8;fori=1:100ifi<16x(i)=exp((-(i-p)^2)/q);elsex(i)=0;endendfori=1:80w(i)=(i-40)/10;fork=1:16dtft(i)=dtft(i)+x(k)*exp(-j*(k-1)*w(i));endendsubplot(1,2,1);');subplot(1,2,2);');p=8;q=8幅频特性6543TFTD3210

p=8;q=8相频特性3210TFTD0-1-2-3-4-2024-4-2024ww2、q=8,p=8,13,14时域分析p=8;q=8;n=0:1:15x=exp(-(n-p).^2/q);stem(x)ylabel('x(n)');xlabel('n');title('p=8,q=4时的时域特性');p=8;q=13;n=0:1:15x=exp(-(n-p).^2/q);stem(x)ylabel('x(n)');xlabel('n');title('p=8,q=4时的时域特性');p=8;q=14;n=0:1:15x=exp(-(n-p).^2/q);stem(x)ylabel('x(n)');xlabel('n');title('p=8,q=4时的时域特性');10.90.80.7

q=8,p=8时的时域特性0.6) 0.5x0.40.30.20.100 2 4 6 8n

10 12 14 1610.90.80.70.6) x0.40.30.2

q=8,p=13时的时域特性0.100 2 4 6 8n

10 12 14 1610.90.80.70.6) x0.40.30.2

q=8,p=14时的时域特性clc;clear

0.100 2 4 6 8n

10 12 14 16q=8;p=8;fori=1:100ifi<16x(i)=exp((-(i-p)^2)/q);elsex(i)=0;endendfori=1:80w(i)=(i-40)/10;fork=1:16dtft(i)=dtft(i)+x(k)*exp(-j*(k-1)*w(i));endendsubplot(1,2,1);');subplot(1,2,2);');q=8,p=8幅频特性6 5 4

q=8,p=8相频特性T T30F F30T TD D2 -11 -20 -3-4-2024-4-2024wwclc;clearq=8;p=13;fori=1:100ifi<16x(i)=exp((-(i-p)^2)/q);elsex(i)=0;endendfori=1:80w(i)=(i-40)/10;fork=1:16dtft(i)=dtft(i)+x(k)*exp(-j*(k-1)*w(i));endendsubplot(1,2,1);');subplot(1,2,2);');4.543.532.5TFTD 1.510.50

q=8,p=13幅频特性

q=8,p=13相频特性43210TFTD0-1-2-3-4-4-2024-4-2024wwclc;clearq=8;p=14;fori=1:100ifi<16x(i)=exp((-(i-p)^2)/q);elsex(i)=0;endendfori=1:80w(i)=(i-40)/10;fork=1:16dtft(i)=dtft(i)+x(k)*exp(-j*(k-1)*w(i));endendsubplot(1,2,1);');subplot(1,2,2);');43.532.5TTD1.510.50

q=8,p=14幅频特性

q=8,p=14相频特性4321TF 0D-1-2-3-4-4-2024-4-2024ww当q不变，p变大时，出现截断效应，当实验中q=8,p=13