數(shù)字信號處理實(shí)驗(yàn)五譜分析

1、實(shí)驗(yàn)五、譜分析一、實(shí)驗(yàn)?zāi)康模貉芯坎煌愋偷拇昂瘮?shù)，研究一些不同的方法來測試窗函數(shù)的性能；專注于有關(guān)窄帶信號的幾個不同的情形。二、實(shí)驗(yàn)原理：信號是無限長的，而在進(jìn)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”看無限長的信號，或者從分析的角度是無限長的信號x(t)乘以有限長的窗函數(shù)w(t)，由傅里葉變換性質(zhì)可知 xtwt12Xj*W(j)如果x(t)是頻帶有限信號，而w(t)是頻帶無限函數(shù)，截斷后的信號也必是頻帶無限信號，從而產(chǎn)生所謂的頻譜泄露。頻譜泄露是不可避免的，但是盡量減小，因此設(shè)計了不同的窗函數(shù)滿足不同的要求。從能量的角度，頻譜

2、泄露也是能量泄露，因?yàn)榧哟昂?，是原來的信號集中在窄頻帶內(nèi)的能量分散到無限的頻帶范圍。1、用MATLAB編程繪制各種窗函數(shù)的形狀。2、用MATLAB編程繪制各種窗函數(shù)的幅度響應(yīng)。3、繪制矩形窗的幅頻響應(yīng)，窗長度分別為：N=10，N=20，N=50，N=100。4、已知周期信號x(t)=0.75+3.4cosft+2.7cos4ft+1.5sin3.5ft+2.5sin7ft，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?yán)L制和比較采用下面窗函數(shù)提取的x(t)的頻譜。三、實(shí)驗(yàn)內(nèi)容：1、用MATLAB編程繪制各種窗函數(shù)的形狀。 w1=boxcar(25); n=0:24;

3、 subplot(221),stem(n,w1),title(矩形窗); w2=hanning(25); subplot(222),stem(n,w2),title(hanning); w3=hamming(25); subplot(223),stem(n,w3),title(hamming); w4=bartlett (25); subplot(224),stem(n,w4),title(bartlett); w5=blackman(25); n=0:24; subplot(221),stem(n,w5),title(blackman); w6=triang(25); subplot(222

4、),stem(n,w6),title(triang); w7=kaiser(25,12); subplot(223),stem(n,w7),title(kaiser); w8=chebwin(25,15); subplot(224),stem(n,w8),title(chebwin);2、用MATLAB編程繪制各種窗函數(shù)的幅度響應(yīng)。Function H,W=dtft(h,N)N=fix(N);If(N fs=10; f=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w=boxcar(N); x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4

5、*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs); y=w.*x; H,W=dtft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=boxcar(N); 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

6、); y=w.*x; H,W=dtft(y,1024); subplot(212);plot(W/2/pi,abs(H),grid;xlabel(frequency),ylabel(magnitude),title(t=1.1Tp);2、漢寧窗 fs=10; f=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w=hanning(N); 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); y=w.*x; H,W=dtft(y,102

7、4); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=hanning(N); 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); y=w.*x; H,W=dtft(y,1024); subplot(212); plot(W/2/pi,abs(H),grid; xlabel(fre

8、quency),ylabel(magnitude),title(t=1.1Tp);3、漢明窗 fs=10; f=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w=hamming(N); 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); y=w.*x; H,W=dtft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitud

9、e),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=hamming(N); 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); y=w.*x; H,W=dtft(y,1024); subplot(212); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=1.1Tp);4、巴特利特窗 fs=10; f=25/16; Tp=2.56; N=

10、0.9*Tp*fs; n=0:N-1; w=bartlett(N); 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); y=w.*x; H,W=dtft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=bartlett(N); x=0.75+3.4*cos(2*

11、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); y=w.*x; H,W=dtft(y,1024); subplot(212); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=1.1Tp);5、布萊克曼窗 fs=10; f=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w=blackman(N); x=0.75+3.4*cos(2*pi*f*n/fs)+2.7*cos(4

12、*pi*f*n/fs)+1.5*sin(3.5*pi*f*n/fs)+2.5*sin(7*pi*f*n/fs); y=w.*x; H,W=dtft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=blackman(N); 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/

13、fs); y=w.*x; H,W=dtft(y,1024); subplot(212); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=1.1Tp);6、triang fs=10; f=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w= triang (N); 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); y=w.*x; H,W=dt

14、ft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w= triang (N); 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); y=w.*x; H,W=dtft(y,1024); subplot(212); plot(W/2/pi,abs(H),grid; x

15、label(frequency),ylabel(magnitude),title(t=1.1Tp);7、kaiser窗 fs=10; f=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w=kaiser (N,18); 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); y=w.*x; H,W=dtft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency)

16、,ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=kaiser (N,18); 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); y=w.*x; H,W=dtft(y,1024); subplot(212); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=1.1Tp);8、切比雪夫窗 fs=10; f

17、=25/16; Tp=2.56; N=0.9*Tp*fs; n=0:N-1; w= chebwin (N,19); 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); y=w.*x; H,W=dtft(y,1024); subplot(211); plot(W/2/pi,abs(H),grid; xlabel(frequency),ylabel(magnitude),title(t=0.9Tp); N=1.1*Tp*fs; n=0:N-1; w=chebwin(N,19); 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