数字信号处理实验五谱分析.docx

1、数字信号处理实验五谱分析一、实验目的：研究不同类型的窗函数，研究一些不同的方法来测试窗函数的性能；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)，由傅里叶变换性质可知 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

2、，因为加窗后，是原来的信号集中在窄频带内的能量分散到无限的频带范围。1、用MATLAB编程绘制各种窗函数的形状。2、用MATLAB编程绘制各种窗函数的幅度响应。3、绘制矩形窗的幅频响应，窗长度分别为：N=10，N=20，N=50，N=100。4、已知周期信号x(t)=0.75+3.4cosft+2.7cos4ft+1.5sin3.5ft+2.5sin7ft，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窗函数提取的x(t)的频谱。三、实验内容：1、用MATLAB编程绘制各种窗函数的形状。 w1=boxcar(25); n=0:24; subplot

3、(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),stem(n

4、,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编程绘制各种窗函数的幅度响应。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*pi*f*n/

5、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); y=w.*

6、x; H,W=dtft(y,1024); subplot(212);plot(W/2/pi,abs(H),grid;xlabel(frequency),ylabel(magnitude),title(t=1.1Tp);2、汉宁窗 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,1024); subp

7、lot(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(frequency),

8、ylabel(magnitude),title(t=1.1Tp);3、汉明窗 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(magnitude),title

9、(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=0.9*Tp*f

10、s; 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*pi*f*n/f

11、s)+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、布莱克曼窗 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*pi*f*n/

12、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/fs); y=w

13、.*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=dtft(y,102

14、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= 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; xlabel(fr

15、equency),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),ylabel(

16、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=25/16;

17、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);

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);四、结果分析：根据不同函数以及不同的要求，根据窗函数的主瓣宽度、频率分辨率、旁瓣的衰减等性能来选择不同的窗函数。由第四题不同窗函数截取的函数的频谱有所不同，而截取1.1T的信号频谱在处为零，而0.9T时则不为零。而其中采样频率决定一周期内的采样点数，也决定了窗的长度，影响了窗的主瓣频宽的大小。