您接收到一些数据,并想知道它是否与您测量的较长的流相匹配。即使数据被噪声破坏,相互关系也能让你做出这样的判断。
将一个环在桌面上旋转的记录加载到工作区中。截取一个一秒钟的片段,然后听一听。
load('Ring.mat')
Time = 0:1/Fs:(length(y)-1)/Fs;
m = min(y);
M = max(y);
Full_sig = double(y);
timeA = 7;
timeB = 8;
snip = timeA*Fs:timeB*Fs;
Fragment = Full_sig(snip);
% To hear, type soundsc(Fragment,Fs)
绘制信号和片段。突出显示片段端点以供参考。
plot(Time,Full_sig,[timeA timeB;timeA timeB],[m m;M M],'r--')
xlabel('Time (s)')
ylabel('Clean')
axis tight
plot(snip/Fs,Fragment)
xlabel('Time (s)')
ylabel('Clean')
title('Fragment')
axis tight
计算并绘制完整信号和片段的相互关系。
[xCorr,lags] = xcorr(Full_sig,Fragment);
plot(lags/Fs,xCorr)
grid
xlabel('Lags (s)')
ylabel('Clean')
axis tight
互相关最大的滞后是信号起始点之间的时间延迟。重新绘制信号,覆盖片段。
[~,I] = max(abs(xCorr));
maxt = lags(I);
Trial = NaN(size(Full_sig));
Trial(maxt+1:maxt+length(Fragment)) = Fragment;
plot(Time,Full_sig,Time,Trial)
xlabel('Time (s)')
ylabel('Clean')
axis tight
重复这一过程,但在信号和片段中分别添加噪声。声音无法从噪音中分辨出来。
NoiseAmp = 0.2*max(abs(Fragment));
Fragment = Fragment+NoiseAmp*randn(size(Fragment));
Full_sig = Full_sig+NoiseAmp*randn(size(Full_sig));
% To hear, type soundsc(Fragment,Fs)
plot(Time,Full_sig,[timeA timeB;timeA timeB],[m m;M M],'r--')
xlabel('Time (s)')
ylabel('Noisy')
axis tight
尽管噪声水平很高,该程序仍能找到丢失的片段。
[xCorr,lags] = xcorr(Full_sig,Fragment);
plot(lags/Fs,xCorr)
grid
xlabel('Lags (s)')
ylabel('Noisy')
axis tight
[~,I] = max(abs(xCorr));
maxt = lags(I);
Trial = NaN(size(Full_sig));
Trial(maxt+1:maxt+length(Fragment)) = Fragment;
figure
plot(Time,Full_sig,Time,Trial)
xlabel('Time (s)')
ylabel('Noisy')
axis tight