I am trying to use the corr2 function of matlab to find the correlation coefficient between two time series data so that I can find the similarity between the two signals.
But I fail to do the same when the signals are of different length and are timeshifted.
DTW is a technique which I can use but I want to know how to compare signals using only correlation in this case.
You just get the numerical values of correlation first for both cases, then you can draw in excel…. I did compare the correlation before and after crisis.. I hope this would help..
Thank you for your quick reply.But I could not get properly.
Say I have two time series signals x=[.,.,.,.,.,.,.,.,.,.,.,......] and y=[.,.,.,.,.,.,.,.,.,.......]
if x=y, I get the correlation coefficient=1 but if I shift the x signal little bit then corelation coefficent comes to about 0.0492 .But in reality I just shifted the similar signal which should not show me much differenence I mean Corelation coefficient should be near about 1say(0.091).
So what is the proper way of finding the similarity between two similar signal which are shifted in time domain.
If you have the signal processing toolbox and are not using 2d-signals you can use XCORR, which gives the evaluated lags as output parameter (use max. lag as the time shift between the two signals).
I used that for synchronizing two signals, and if that is what you are aiming to do, then XCORR will be your friend!
http://de.mathworks.com/help/signal/ref/xcorr.html
Our Paper "The Modified R a Robust Measure of Association for Time Series The Modified R a Robust Measure of Association for Time Series" may be useful for you because simple correlation coefficient is not a valid measure for time series data.
You will need to compensate the signals for the time shift before calculating the correlation. The function xcorr will help you as suggested by David above. The two signals need to have the same length to be able to calculate the correlation.
I am not sure why you shift your signal in the first place though? If that is what you want to do then obtaining a lower correlation coefficient is correct as long as the two signals are "less" in phase than they were before.
Costanzo
I am not sure exactly what Your problem is, but here is a description of the basic process of finding unknown correlation coefficients in signals the way I am used to think about it.
If You know the time shift exactly, simply time shifting the time series and cross correlation of the 2 resulting time series gives You the correlation coefficient. Also make sure that the samples are long enough to contain the features You try to correlate. Akin to the sampling theorem for FFT. Make sure You have high enough sample rate. Windowing and truncation of the time signals has to be done sensibly. Using to long time series just wastes computational resources.
But if You don´t know the exact time shift, You need to find the cross correlation curve as a function of different time shifts. This gives you a 2 dimensional surface if You do this over time. Then You can find the peaks and analyze the properties of the signal over time. If You have just one large ridge, the amplitude is the correlation coefficient if it is constant over time, and You can determine the time shift rather accurately by analyzing this shape. The shape of the correlation curve also gives You some information on the spectral content of the signal.
Hope this helps
Try running an LMS adaptive filter using the signal you believe to be the earliest as the reference, and the later signal as the desired. After convergence, the taps of the adaptive filter will tell you all sorts of things about the relationship between the two signals. The delay between the signals will be the most valuable information. If you have the signals captured, then you can re-run the process over and over with smaller and smaller step sizes to hone in on a near perfect impulse response.
In echo cancellation, we use the sqrt(sum(h^2)) as a measure of the overall correlation.
Three things might trip this whole process up.
1) The one signal has some very seriously non-linear relationship to the other. LMS assumes a linear channel.
2) If you know the signal are correlated, but you get poor results, then simply switch the reference and the desired signals as the delays may be reversed., or you may have attempted to equalize rather then canceler the signal.
3) For this to work, the system must be causal. Sometimes I have had to delete samples at the beginning of one or other signal to force causality. If you keep track of how many samples you deleted, then you can add this back to determine the real delay.
Regard,
David
[op lags] = xcorr(inputVariable, output, numoflags);
lags= lags';
plot(op,lags);
ideally op will be (numoflags*2)+1 since it runs from -numoflags to +numoflags
the lag at which you have maximum op is the number of time steps you have to shift (forward or backward based in the sign of lags).
I am not an expert in this area... But just thinking out loud.
How about sampling the signals long enough, run Fourier analysis and see how similar the Fourier coefficients are... If the time-series is periodic, and if your sampling time is greater than the time-period, I think you will get the basic frequencies in the right order....
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