I think this is a relevant candidate for Higher order statistics (HOS) methods. Compute the higher order moments or cumulants. they should discriminate the 2 signals. If you are suggesting the centroid as the (first) mean, this is exactly the deficient method in view of HOS

I think high order statistics is a very elegant and valid solution. If I understand your problem right, I can say that I would likely try a somewhat less elegant way: Cross-correlation of the two signals for registration and then Pearson correlation or sum of squared differences of the two signals as a measure of likelyhood.

Phase correlation of the signals is usually quite a good method if you can model the shifting parameters between them. If the signals are one dimensional and shifted in time, Phase correlation is very easy and gives excellent results, since it is quite robust to "some" types of noise.

hi david

i have signals recorded repeatedly using my phone. These are tri-axial acceleration data. The data contains . Time in milliseconds and accelerations in meter/second^2. I have data for same sample recorded on different days. The signals seems alike visually. but when statistically tested using ttest it shows not similar. This is one scene.

Secondly, i recorded data on two different phones. These are shown differently visually as well as statistically. Here in this case, problem is the start time of recording in both phones is different. I want to find one common point of start. This is one question. This is i think registration of two signals to common point.Right?

More question is , how to solve different time interval problem? This means the recording interval is 50milliseconds. But the data recorded sometimes not after 50milliseconds. i want it to be after 50millicseconds. Should i use resampling first? Please suggest.

Hi Rajiv,

you may want to read about the idea of cepstrum. It might be useful especially if two signals coming from one device have a degree of overlap (the second signal begins before the first has ended).

NB yes it's cepstrum, not spectrum.

Hope this helps - Leszek.

for your micrphone, you should use intercorrelation to find common start time.

I dont understand your time interval problem.. If it is just a translation, you can observe problem causality and just add zero value at the beginning.

Hi Julien,

do you mean cross-covariance? I tried using cross-correlation and can get only samples lagging or leading from one signal to other. But it is only upto first highest matching peak in two signals. It doesn't seem work.

I add zeros at the signal that lags but the plot doesn't show matching peaks of two signals. The length of signals (number of samples) also changes but not being same. can we make the length same also?

thanks in advance.

Rajiv

I mean cross-correlation, intercorrelation is the french term.

If you don't fint a correct match after a cross correlation, it is because your signal should have numerous echoes... to avoid them, you can work on echo cancellation using sceptrum or adaptive filter...

For the zeros they can be added at the beginning or at the end. For the beginning it is just causality but for the end you have to ensure that the signal is quite flat before adding zeros.

Hello Rajiv,

I think the problem (or the solution to your problem) is somewhere else.

From your discussions so far with several members, I guess that all of the attention is focused on the statistical analysis of the signals to find one common starting point in your data for comparison and analysis. Also, it seems very clearly that you are confused with the sampling of the signal/s.

From the description of your work I understand that you are having at least one sensor (accelerometer) with 3 signals (x,y,z axis). May be other phone means a second sensor in picture with 3 additional (6 total) channels for signal acquisition. What you are doing is sampling these channels at 50ms interval and trying to find a common starting point for the signal or data logged.

If my understanding of your system is correct as above, read further.

1) The problem you are facing in finding one common starting point for your data is that you are using sequential sampling of the channels. That is, every sample is acquired 50ms after the other. That is why you are not able to compare all the channels (or the data) using any of the proven statistical methods.

2) So the actual problem lies with the hardware, i.e. the way you are sampling your signal.

3) As you have 3 channels (for one sensor) then your first sample (data) comes at say t=0. Then second comes at 50ms and the third arrives at 100ms.

4) So what you are looking at is not the same event from all 3 channels at the same time but different events at different times. Then you would never be able make any comparison with the signal/s no matter how best method you apply.

5) So your problem can be defined as the ERROR DUE TO SEQUENTIAL SAMPLING"

6) Solution: Try SIMULTANEOUS SAMPLING i.e. acquire every sample (or data) for all the channels at the same time. This should not only give you common starting point but all your channel sampling will be with respect to one common time axis. I believe, this is what you want to happen.

7) If you try this simultaneous sampling, then apply any of the methods that you have tried and see what happens.

8) DO NOT FORGET to inform if this idea really helped you or not.

9) If you have any further question or need help feel free to ask for clarification.

Thanks and wish you all the best.!

-Prasanna Waichal

hi prasanna

i have to start manually the recording/logging of data from one installed application on my mobile.

How is it possible to start the recording on two different sensors manually? This is human tendency to make gap between two simultaneous pressing the buttons. How that time difference to adjust?

Thanks

Rajiv

Hi Rajiv,

I understood your question and also I have worked similar problem.You can use cross correlation or coherence to check the similarity and dissimilarity of two signals and also you can use wavelet transform to perform this analysis.For understanding refer my paper in my page.

Hello Rajiv,

As I understand, you are using the sensors in a mobile phone and running one software application to capture/log the data. And it is also a true that your second sensor is in another mobile phone – So, under this condition, I do not think, you will ever be able to handle the two sensors from one software.

Secondly, using two manually controlled switches is also not at all a solution for your requirement.

I do not know what exactly you want to achieve by collecting this data, nor what level of research you are working for - A PhD, or Masters or Undergraduate?

But try to pay attention to one important fact that even though you may have best software available, the hardware (sensor electronics) in a mobile phone is all pre-wired and pre-configured. These accelerometers are not only the sensors but have some intelligent functionalities implemented by a built-in processor. What you get at the output is the digital data communicated by the processor. Therefore you may not be knowing, how the sensor output is handled – sequential or simultaneous?

My final and best advice to you will be to look for such stand-alone accelerometer chips or choose different sensors (X-Y-Z analog output) and have a dedicated sampling system to log your data. Keep it in mind – Agar kuwe mein nahi hai to balti mein kahan se ayega? – meaning if you do not have it in the well, where will you get water in your bucket?

So unless you have a reliable sensor hardware and the data, you software efforts will not yield the desired result.

If you need any further help write a mail and I shall be happy to give you a solution. Wish you best of luck!

Thanks,