%例程5－3  計算隨機信號的自相關函數和互相關函數
% e.g.5-3.m for example5-3;
% to test function of xcorr;
 
clear all;
N=10^3;
n=[0:N-1];
Fs=500;
t=n/Fs;
Mlag=100;
% Generate noise
x1=randn(1,length(t));
figure(1);plot(t,x1);
xlabel('n'); ylabel('x1(n)');
title('Original noise x1');
grid on;
% Computing the unbiased atuocorretaion of x1
[r1,lags]=xcorr(x1,Mlag,'unbiased');
figure(2); plot(lags/Fs,r1);
xlabel('n'); ylabel('Rx1(n)');
title('Autocorrelation of x1');
grid on;
% Generate signal plus noise
x2=sin(2*pi*10*t)+0.7*randn(1,length(t));
figure(3);  plot(t,x2);
xlabel('n'); ylabel('x2(n)');
title('Original signal x2');
grid on;
% Computing the unbiased atuocorretaion of x2
[r2,lags]=xcorr(x2,Mlag,'unbiased');
figure(4); plot(lags/Fs,r2);
xlabel('n'); ylabel('Rx2(n)');
title('Autocorrelation of x2');
grid on;
[corrx1x2,lags]=xcorr(x1,x2,Mlag,'unbiased');
figure(5);plot(lags/Fs,corrx1x2);
title('Cross-Correlation of x1 and x2');
grid on;