Peak-finding algorithm for Python SciPy

Question

I can write something myself by finding zero-crossings of the first derivative or something  but it seems like a common-enough function to be included in standard libraries   Anyone know of one   My particular application is a 2D array  but usually it would be used for finding peaks in FFTs  etc   Specifically  in these kinds of problems  there are multiple strong peaks  and then lots of smaller  peaks  that are just caused by noise that should be ignored   These are just examples  not my actual data   1-dimensional peaks     2-dimensional peaks     The peak-finding algorithm would find the location of these peaks  not just their values   and ideally would find the true inter-sample peak  not just the index with maximum value  probably using quadratic interpolation or something   Typically you only care about a few strong peaks  so they d either be chosen because they re above a certain threshold  or because they re the first n peaks of an ordered list  ranked by amplitude   As I said  I know how to write something like this myself   I m just asking if there s a pre-existing function or package that s known to work well   Update   I translated a MATLAB script and it works decently for the 1-D case  but could be better   Updated update   sixtenbe created a better version for the 1-D case

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First things first  the definition of  peak  is vague if without further specifications   For example  for the following series  would you call 5-4-5 one peak or two   1-2-1-2-1-1-5-4-5-1-1-5-1  In this case  you ll need at least two thresholds  1  a high threshold only above which can an extreme value register as a peak  and 2  a low threshold so that extreme values separated by small values below it will become two peaks   Peak detection is a well-studied topic in Extreme Value Theory literature  also known as  declustering of extreme values    Its typical applications include identifying hazard events based on continuous readings of environmental variables e g  analysing wind speed to detect storm events

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To detect both positive and negative peaks  PeakDetect is helpful  from peakdetect import peakdetect  peaks   peakdetect data  lookahead 20     Lookahead is the distance to look ahead from a peak to determine if it is the actual peak     Change lookahead as necessary  higherPeaks   np array peaks 0   lowerPeaks   np array peaks 1   plt plot data  plt plot higherPeaks   0   higherPeaks   1    ro   plt plot lowerPeaks   0   lowerPeaks   1    ko

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For those not sure about which peak-finding algorithms to use in Python  here a rapid overview of the alternatives  https   github com MonsieurV py-findpeaks  Wanting myself an equivalent to the MatLab findpeaks function  I ve found that the detect peaks function from Marcos Duarte is a good catch   Pretty easy to use   import numpy as np from vector import vector  plot peaks from libs import detect peaks print  Detect peaks with minimum height and distance filters    indexes   detect peaks detect peaks vector  mph 7  mpd 2  print  Peaks are   s     indexes     Which will give you

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There is a function in scipy named scipy signal find peaks cwt which sounds like is suitable for your needs  however I don t have experience with it so I cannot recommend    http   docs scipy org doc scipy reference generated scipy signal find peaks cwt html

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There are standard statistical functions and methods for finding outliers to data  which is probably what you need in the first case  Using derivatives would solve your second  I m not sure for a method which solves both continuous functions and sampled data  however

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The function scipy signal find peaks  as its name suggests  is useful for this  But it s important to understand well its parameters width  threshold  distance and above all prominence to get a good peak extraction   According to my tests and the documentation  the concept of prominence is  the useful concept  to keep the good peaks  and discard the noisy peaks   What is  topographic  prominence  It is  the minimum height necessary to descend to get from the summit to any higher terrain   as it can be seen here     The idea is      The higher the prominence  the more  important  the peak is    Test     I used a  noisy  frequency-varying sinusoid on purpose because it shows many difficulties  We can see that the width parameter is not very useful here because if you set a minimum width too high  then it won t be able to track very close peaks in the high frequency part  If you set width too low  you would have many unwanted peaks in the left part of the signal  Same problem with distance  threshold only compares with the direct neighbours  which is not useful here  prominence is the one that gives the best solution  Note that you can combine many of these parameters   Code   import numpy as np import matplotlib pyplot as plt  from scipy signal import find peaks  x   np sin 2 np pi  2  np linspace 2 10 1000   np arange 1000  48000    np random normal 0  1  1000    0 15 peaks      find peaks x  distance 20  peaks2      find peaks x  prominence 1         BEST  peaks3      find peaks x  width 20  peaks4      find peaks x  threshold 0 4        Required vertical distance to its direct neighbouring samples  pretty useless plt subplot 2  2  1  plt plot peaks  x peaks    xr    plt plot x   plt legend   distance    plt subplot 2  2  2  plt plot peaks2  x peaks2    ob    plt plot x   plt legend   prominence    plt subplot 2  2  3  plt plot peaks3  x peaks3    vg    plt plot x   plt legend   width    plt subplot 2  2  4  plt plot peaks4  x peaks4    xk    plt plot x   plt legend   threshold    plt show

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Detecting peaks in a spectrum in a reliable way has been studied quite a bit  for example all the work on sinusoidal modelling for music audio signals in the 80ies  Look for  Sinusoidal Modeling  in the literature   If your signals are as clean as the example  a simple  give me something with an amplitude higher than N neighbours  should work reasonably well  If you have noisy signals  a simple but effective way is to look at your peaks in time  to track them  you then detect spectral lines instead of spectral peaks  IOW  you compute the FFT on a sliding window of your signal  to get a set of spectrum in time  also called spectrogram   You then look at the evolution of the spectral peak in time  i e  in consecutive windows

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I m looking at a similar problem  and I ve found some of the best references come from chemistry  from peaks finding in mass-spec data    For a good thorough review of peaking finding algorithms read this   This is one of the best clearest reviews of peak finding techniques that I ve run across    Wavelets are the best for finding peaks of this sort in noisy data     It looks like your peaks are clearly defined and aren t hidden in the noise   That being the case I d recommend using smooth savtizky-golay derivatives to find the peaks  If you just differentiate the data above you ll have a mess of false positives     This is a very effective technique and is pretty easy to implemented  you do need a matrix class w  basic operations    If you simply find the zero crossing of the first S-G derivative I think you ll be happy

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I do not think that what you are looking for is provided by SciPy   I would write the code myself  in this situation   The spline interpolation and smoothing from scipy interpolate are quite nice and might be quite helpful in fitting peaks and then finding the location of their maximum

[python] Peak-finding algorithm for Python/SciPy

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