Solved – Statistical comparison of two signals

cross correlationfrequencysignal processingtime series

I need to develop an algorithm that will compare two signals and generate some metric(s) to describe changes between them. Signal processing and analysis isn’t my strong point so I would appreciate any help!

Here is an example of what the signals look like:

Signal example

The signal starts at a constant amplitude, then transitions into a lower amplitude before transitioning back up to the same constant amplitude as the start. The part in the middle is the region of interest, which is what needs to be analysed. Some of the differences that I am expecting (all within the region of interest) are:

  1. Mean amplitude of the area of interest, relative to the start and end amplitudes
  2. Slope of fall/rise transitions and of individual peaks and troughs
  3. Number of peaks and troughs

The algorithm needs to output some generic metrics which can be used to quantify changes in any or all of these parameters. Any guidance on what method(s) I could use to do this would be a great help. I know a little about cross-correlation and have heard about wavelet transform analysis, but I am wondering if these are appropriate, or if there are other methods that would work better.

Best Answer

Time series analysis incorporating both ARIMA structure and empirically identifiable deterministic structure (level shifts/local time trends.seasonal pulses and pulses) might be of some use to you http://www.unc.edu/~jbhill/tsay.pdf. Good analytics/software should/could identify 2 level shifts ( 3 regimes) which would be important starting point for your analysis providing "the region of interest". If you wish you can post your data and I will try and demonstrate that to you and the list.

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