# pattern recognition in a time series

I understand that the question I am asking seem the be somewhat related to another question which has been asked already.

But I feel that this is an entirely different question.

I have a huge (over 100K data points) time series data of the position (x, y coordinates) of an element in space. This element is vibrating randomly, and both amplitude and the frequency of vibration is random. I want to look at the vibrations which are similar and see if there is any pattern in those vibrations, are they periodic or related somehow.

I am working on a biological problem and have very little knowledge about signal processing. I can provide more details Any help would be really appreciated.

• If you treat an x,y coordinate as complex number (x+yi,) then you could do a complex fft on a sequence of coordinates. This would give you information about periodicity and the amplitude - that is, you could find the vibrational frequencies present and the amplitudes. Autocorrelation might also be of use - if the result is pretty much flat then the vibration is random, peaks tell you how often some patterns repeat. Do you have any sample data you could post?
– JRE
Jan 8, 2015 at 14:30
• Thanks a lot, I will try that. Meanwhile, I have uploaded a sample data set here: (dropbox.com/s/zv2lgbaindewwo6/TestData_2_2_061732.csv?dl=0)
– C.M
Jan 8, 2015 at 14:58
• I converted your data to a wav file and fed it into Baudline. The complex FFT doesn't show anything like a clear periodicity -looks like noise. Autocorrelation shows some (very) weak correlations over some long periods. This doesn't say that there are no stretches that repeat, but if they do they are few and not strongly similar. The data seem to be very coarsely sampled - this might mask the real signal.
– JRE
Jan 8, 2015 at 20:35
• @JRE: Thanks a lot for your efforts. Yes, the data is coarsely sampled, but even at this sampling rate I generate TeraBytes of data per dataset, so its very difficult to sample more than this. Said that, I also was not able to pull any periodicity sing FFT / auto correlations. I was wondering if it would make better sense we limit the frequencies to lets say less than 15Hz and then try looking for something. I know that frequencies over 15Hz are not relevant, so anything beyond that can be skipped.
– C.M
Jan 9, 2015 at 7:51
• By "coarsely sampled" I was referring the resolution of the numbers - you have the equivalent of 4 bits, maybe 5 bits of resolution. What is your sampling rate (samples per second?)
– JRE
Jan 9, 2015 at 8:00