Peak detection algorithm in Python

Question

I'm implementing a peak detection algorithm in Python that detects only those peaks that are above a threshold magnitude. I don't want to use the inbuilt function as I have to extend this simulation to Hardware implementation also.

from math import sin,isnan
from pylab import *

def peakdet(v, delta,thresh,x):
    delta=abs(delta)
    maxtab = []
    mintab = []

    v = asarray(v)

    mn, mx = v[0], v[0]
    mnpos, mxpos = NaN, NaN

    lookformax = True

    for i in arange(len(v)):
        this = v[i]
        if abs(this)>thresh:
            if this > mx:
                mx = this
                mxpos = x[i]
            if this < mn:
                mn = this
                mnpos = x[i]
            if lookformax:
                if (this < mx-delta):
                    if (mx>abs(thresh)) and not isnan(mxpos):
                        maxtab.append((mxpos, mx))
                    mn = this
                    mnpos = x[i]
                    lookformax = False
            else:
                if (this > mn+delta):
                    if (mn<-abs(thresh)) and not isnan(mnpos):
                        mintab.append((mnpos, mn))
                    mx = this
                    mxpos = x[i]
                    lookformax = True
    return array(maxtab), array(mintab)

#Input Signal
t=array(range(100))
series=0.3*sin(t)+0.7*cos(2*t)-0.5*sin(1.2*t)

thresh=0.95 #Threshold value
delta=0.0 #

a=zeros(len(t)) #
a[:]=thresh #

maxtab, mintab = peakdet(series,delta,thresh,t)

#Plotting output
scatter(array(maxtab)[:,0], array(maxtab)[:,1], color='red')
scatter(array(mintab)[:,0], array(mintab)[:,1], color='blue')
xlim([0,t[-1]])
title('Peak Detector')
grid(True)
plot(t,a,color='green',linestyle='--',dashes=(5,3))
plot(t,-a,color='green',linestyle='--',dashes=(5,3))
annotate('Threshold',xy=(t[-1],thresh),fontsize=9)
plot(t,series,'k')
show()

The problem with this program is that it is unable to detect some peaks even though they are above the threshold. This is the output I got:

I saw other posts with peak detection problems but couldn't find any solution. Please help and suggest corrections.

Answer 1

Solution with find_peaks from scipy.signal

from scipy.signal import find_peaks
import numpy as np
import matplotlib.pyplot as plt

# Input signal
t = np.arange(100)
series = 0.3*np.sin(t)+0.7*np.cos(2*t)-0.5*np.sin(1.2*t)

# Threshold value (for height of peaks and valleys)
thresh = 0.95

# Find indices of peaks
peak_idx, _ = find_peaks(series, height=thresh)

# Find indices of valleys (from inverting the signal)
valley_idx, _ = find_peaks(-series, height=thresh)

# Plot signal
plt.plot(t, series)

# Plot threshold
plt.plot([min(t), max(t)], [thresh, thresh], '--')
plt.plot([min(t), max(t)], [-thresh, -thresh], '--')

# Plot peaks (red) and valleys (blue)
plt.plot(t[peak_idx], series[peak_idx], 'r.')
plt.plot(t[valley_idx], series[valley_idx], 'b.')

plt.show()

The resulting plot is shown below.

Note that find_peaks has a parameter height which is what we here called thresh. It also has a parameter called threshold, which is doing something else.

Documentation for find_peaks

Answer 2

Your function uses quite a lot of parameters. You can decompose the problem to a few steps:

1. First detect all points above the threshold. Add those points to a maxthresh and minthresh list.
2. Iterate through the maxthresh list and if the y value prior to the point is less than the point, and the y value after the point is less than the point, then the point is a peak.
3. Iterate through the minthresh list and if the y value prior to the point is greater than the point, and the y value after the point is greather than the point, then the point is a peak.

Code implementation:

from math import sin
from matplotlib import pylab
from pylab import *

def peakdet(v, thresh):
    maxthresh = []
    minthresh = []
    peaks = []
    valleys = []

    for x, y in v:
        if y > thresh:
            maxthresh.append((x, y))
        elif y < -thresh:
            minthresh.append((x, y))

    for x, y in maxthresh:
        try:
            if (v[x - 1][1] < y) & (v[x + 1][1] < y):
                peaks.append((x, y))
        except Exception:
            pass

    for x, y in minthresh:
        try:
            if (v[x - 1][1] > y) & (v[x + 1][1] > y):
                valleys.append((x, y))
        except Exception:
            pass

    return peaks, valleys

Testing the code:

# input signal
t = array(range(100))
series = 0.3 * sin(t) + 0.7 * cos(2 * t) - 0.5 * sin(1.2 * t)

arr = [*zip(t, series)]  # create a list of tuples where the tuples represent the (x, y) values of the function
thresh = 0.95

peaks, valleys = peakdet(arr, thresh)

scatter([x for x, y in peaks], [y for x, y in peaks], color = 'red')
scatter([x for x, y in valleys], [y for x, y in valleys], color = 'blue')
plot(t, 100 * [thresh], color='green', linestyle='--', dashes=(5, 3))
plot(t, 100 * [-thresh], color='green', linestyle='--', dashes=(5, 3))
plot(t, series, 'k')
show()

Additional test to make sure peak is detected when multiple points above threshold:

# input signal
t = array(range(100))
series = 6.3 * sin(t) + 4.7 * cos(2 * t) - 3.5 * sin(1.2 * t)

arr = [*zip(t, series)]
thresh = 0.95

peaks, valleys = peakdet(arr, thresh)

scatter([x for x, y in peaks], [y for x, y in peaks], color = 'red')
scatter([x for x, y in valleys], [y for x, y in valleys], color = 'blue')
plot(t, 100 * [thresh], color='green', linestyle='--', dashes=(5, 3))
plot(t, 100 * [-thresh], color='green', linestyle='--', dashes=(5, 3))
plot(t, series, 'k')
show()

Answer 3

So, here you have a numpythonic solution (which is much better than doing a loop explicitly).

I use the roll function to shift the numbers +1 or -1 in the position. Also a "peak" is defined as a local maximum, where the previous and posterior number are smaller than the central value.

The full code is:

import numpy as np
import matplotlib.pyplot as plt

# input signal
x = np.arange(1,100,1)
y = 0.3 * np.sin(x) + 0.7 * np.cos(2 * x) - 0.5 * np.sin(1.2 * x)
threshold = 0.95

# max
maxi = np.where(np.where([(y - np.roll(y,1) > 0) & (y - np.roll(y,-1) > 0)],y, 0)> threshold, y,np.nan)
# min
mini = np.where(np.where([(y - np.roll(y,1) < 0) & (y - np.roll(y,-1) < 0)],y, 0)< -threshold, y,np.nan)

if you plot it, you get:

Answer 4

these code

        if lookformax:
            if (this < mx-delta):
                if (mx>abs(thresh)) and not isnan(mxpos):
                    maxtab.append((mxpos, mx))
                mn = this
                mnpos = x[i]
                lookformax = False
        else:
            if (this > mn+delta):
                if (mn<-abs(thresh)) and not isnan(mnpos):
                    mintab.append((mnpos, mn))
                mx = this
                mxpos = x[i]
                lookformax = True

only run under the condition

    if abs(this)>thresh:

so your can only find a peak when the next point above the thresh is smaller than it.

put it out the condition