[python] Peak-finding algorithm for Python/SciPy

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:

enter image description here

The idea is:

The higher the prominence, the more "important" the peak is.

Test:

enter image description here

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()

Examples related to python

programming a servo thru a barometer Is there a way to view two blocks of code from the same file simultaneously in Sublime Text? python variable NameError Why my regexp for hyphenated words doesn't work? Comparing a variable with a string python not working when redirecting from bash script is it possible to add colors to python output? Get Public URL for File - Google Cloud Storage - App Engine (Python) Real time face detection OpenCV, Python xlrd.biffh.XLRDError: Excel xlsx file; not supported Could not load dynamic library 'cudart64_101.dll' on tensorflow CPU-only installation

Examples related to scipy

Reading images in python Numpy Resize/Rescale Image How to get the indices list of all NaN value in numpy array? ImportError: cannot import name NUMPY_MKL numpy.where() detailed, step-by-step explanation / examples Scikit-learn train_test_split with indices Matplotlib: Specify format of floats for tick labels Installing NumPy and SciPy on 64-bit Windows (with Pip) Can't install Scipy through pip Plotting a fast Fourier transform in Python

Examples related to fft

only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices Plotting a fast Fourier transform in Python How to plot a 2D FFT in Matlab? Understanding Matlab FFT example FFT in a single C-file How do I obtain the frequencies of each value in an FFT? Reliable and fast FFT in Java Peak-finding algorithm for Python/SciPy An implementation of the fast Fourier transform (FFT) in C#

Examples related to hough-transform

Peak-finding algorithm for Python/SciPy