CODEWITHSUNDEEP
arraysalgorithmsignalssignal-processingperiodicity
David Ferris
David Ferris

Reputation: 2325

An Algorithm Comparing Peaks: are they in phase or not?

I am developing an algorithm for comparing two lists of numbers. The lists represent peaks discovering in a signal using a robust peak detection method. I wish to come up with some way of determining whether the peaks are either in phase, out of phase, or neither (could not be determined). For example:

These arrays would be considered in phase:

[ 94 185 278 373 469], [ 89 180 277 369 466]

But these arrays would be out of phase:

[51 146 242 349], [99 200 304 401]

There is no requirement that the arrays must be the same length. I have looked into measuring periodicity, however in this case I can assume the signal is already periodic.

Another idea I had was to divide all the array elements by their index (or their index+1) to see if they cluster around one or two points, but this is not robust and fails if a single peak is missing.

What approaches might be useful in solving this problem?

Upvotes: 1

Views: 72

Answers (2)

hotpaw2
hotpaw2

Reputation: 70733

I would enter the peak locations, using them as index locations, into a much larger array (best if the length of the array is close to an integer multiple of the periodicity distance of your peaks), and then do either a complex Goertzel filter (if you know the frequency), or do a DFT or FFT (if you don't know the frequency) of the array. Then use atan2() on the complex result (at the peak magnitude frequency for the FFT) to measure phase relative to the array starts. Then compare unwrapped phases using some difference threshold.

Upvotes: 0

Peter de Rivaz
Peter de Rivaz

Reputation: 33509

One approach would be to find the median distance from each peak in the first list to a peak in the second list.

If you divide this distance by the median distance between peaks in the first list, you will get a fraction where 0 means in phase, and 0.5 means out of phase.

For example:

[ 94 185 278 373 469], [ 89 180 277 369 466]
94->89 = 5
185->180 = 5
278->277 = 1
373->369 = 4
469->466 = 5

Score = median(5,5,1,4,5) / median distance between peaks
      = 5 / 96 = 5.2% => in phase


[51 146 242 349], [99 200 304 401]
51->99 = 48
146->99 = 47
242->200 = 42
349->304 = 45
score = median(48,47,42,45) / median distance between peaks
      = 46 / 95.5
      = 48% => out of phase

Upvotes: 2

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