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?
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