I am trying to look for significant peaks/spikes and periodic changes or fluctuations in about 60 time series of synthetic data.
For example, in data1
below, there are two large peaks around points 8 and 46, and I would like to be able to quantitatively find peaks like those, even if not quite so exaggerated.
I'm also trying to look for periodicity in something like data2
and get the period/amplitude if possible.
I'm trying to use Fourier, but it's giving me some issues. It's not showing obvious spikes at all; it's very possible that I'm just using Fourier wrong, or that I shouldn't be using Fourier. So now I'm here. Does anyone know how I should be able to do this? Thank you!
data1={0,0,0,0.000961538,0.00308404,0.000946074,0.004020101,0.004048583,0.002070393,0.00260078,0.000633714,0.001686341,0.001239926,0.00199071,0.001218769,0,0.001264223,0.001207001,0.00119976,0.001162791,0,0.001054296,0.001402525,0.000917852,0,0.000417537,0,0.0003861,0.000365097,0.000347102,0.000344471,0.000333,0,0.000308833,0.000605694,0.000288101,0.00110957,0.000558036,0.001787995,0.000485201,0.000942063,0.001139991,0.001303215,0.002961709,0.002135093,0.00387311,0.003771644,0.001746586,0.002402763,0.001606308,0.001939595,0.001298364,0.001393566,0.000666815,0.001298842,0.001331558};
data2={0,0.00174216,0,0.002298851,0.001904762,0.001106195,0.003468208,0.002915452,0.004642526,0.002629273,0.003218021,0.003843198,0.00620155,0.005426357,0.010140406,0.003875969,0.003443526,0.00433526,0.004837595,0.007064868,0.003858521,0.001960784,0.006638503,0.004376368,0.003757381,0.004495504,0.004627249,0.004975124,0.002912621,0.003063457,0.007327586,0.005225653,0.005793226,0.005009107,0.005033557,0.00802139,0.006254599,0.005382131,0.007531107,0.007951654,0.007968127,0.007910929,0.010520637,0.012363636,0.012119826,0.012159934,0.012415131,0.014611237,0.014464802,0.017215343,0.018433818,0.016375,0.016557475,0.015978552,0.017170891,0.018142163}
EDIT: Originally omitted data1
. Added those data.
Fourier
is assumed to be one period of a periodic signal. Try function likeFindPeaks
, if it can be tuned to suit your needs. $\endgroup$data2
has a clear upward trend. Not obvious what is wanted for a set like that (e.g. whether the trend should first be removed). If more information were provided about the desired outcome, type of data, and the like that would be helpful. $\endgroup$