用matlab语言产生一个正弦信号，进行频谱分析和自相关分析，求教~~~~~谢谢啊

Question

用matlab语言产生一个正弦信号，该信号由不同频率并且幅值也不同的正弦信号组成，对该信号进行频谱分析和自相关分析，并与白噪声信号进行互相关分析。

Answer 1

下面matlab程序，按照你的要求编写的。

fs=100;N=200;

lag=100;

%randn('state',0);   %设置产生随机数的初始状态（噪声）

n=0:N-1;t=n/fs;

x1=sin(2*pi*10*t)+2*sin(2*pi*15*t)  

y=fft(x1,N);                                  %计算频谱

mag=abs(y);

f=n*fs/N;

figure(1)

subplot(2,2,1),plot(t,x1);

title('原始信号'),xlabel('时间/s');

subplot(2,2,2),plot(f(1:N/2),mag(1:N/2)*2/N);

title('频谱图'),xlabel('频率/Hz');

[c,lags]=xcorr(x1,lag,'unbiased');             % 自相关

subplot(2,2,3),plot(lags/fs,c);

title('自相关信号'),xlabel('时间/s');

m=length(c)-1;                            

z=fft(c,m);                                  

mag_z=abs(z);

ff=(0:m-1)*fs/m;

subplot(2,2,4),plot(ff(1:m/2),mag_z(1:m/2)*2/m);

title('自相关频谱'),xlabel('频率/Hz');

figure(2)

[c1,lags1]=xcorr(x1,randn(1,length(t)),lag,'unbiased'); 

m1=length(c1)-1;                            

z1=fft(c1,m1);                                  

mag_z1=abs(z1);

ff1=(0:m1-1)*fs/m1;

subplot(2,1,1),plot(lags1/fs,c1);

title('互相关信号'),xlabel('时间/s');

subplot(2,1,2),plot(ff1(1:m1/2),mag_z1(1:m1/2)*2/m1);

title('互相关频谱'),xlabel('频率/Hz');

Answer 2

% The number of data points for y should be power of 2, and
% truncation is needed to achieve the requirement
%--------------------------------------------------------------------------
% (1) Compute number of data points and sampling time interval
%--------------------------------------------------------------------------
ntime=max(size(t));
dt=(t(1,ntime)-t(1,1))/(ntime-1);
%--------------------------------------------------------------------------
% (2) Truncate the data points of y
%--------------------------------------------------------------------------
% Extract data points at the power of 2. Truncate extra data points
% so that the final number of data points is in the power of two and
% also as close as possible to the given number of data points
N=fix(log10(ntime)/log10(2))
%--------------------------------------------------------------------------
% (3) Calculate FFT
%--------------------------------------------------------------------------
% Calculate FFT of the time domain data and
% take absolute values of the result
yfft=fft(y(1:2^N,:));
yfft=abs(yfft(1:2^N/2,:))*dt;
%--------------------------------------------------------------------------
% (4) Calculate frequency vector
%--------------------------------------------------------------------------
% Set up the frequency scale from the given sampling interval.
% Apply the Nyquist criterion to establish the maximum frequency
freq0=0;
freqf= (1/dt)/2; % Maximum or final frequency value
df=freqf/(2^N/2); % Frequency interval

freq=0:df:freqf-df; % Frequency axis values