Python 中的峰值检测算法

Question

我正在 Python 中实施峰值检测算法，该算法仅检测那些高于阈值幅度的峰值。我不想使用内置函数，因为我还必须将此模拟扩展到硬件实现。

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()

这个程序的问题是它无法检测到一些峰值，即使它们高于阈值。这是我得到的输出：

我看到其他帖子有峰值检测问题，但找不到任何解决方案。请帮助并提出更正建议。

Answer 1

这些代码

        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

仅运行条件下

    if abs(this)>thresh:

所以你只能在阈值上方的下一个点小于它时找到一个峰值。

放出条件

Answer 2

您的函数使用了很多参数。您可以将问题分解为几个步骤：

首先检测所有高于阈值的点。将这些点添加到 maxthresh 和 minthresh 列表中。
遍历maxthresh列表，如果该点之前的y值小于该点，且该点之后的y值小于该点，则该点为峰。
遍历minthresh列表，如果该点之前的y值大于该点，且该点之后的y值大于该点，则该点为峰。

代码实现：

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

测试代码：

# 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()

额外测试以确保在多个点高于阈值时检测到峰值：

# 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

所以，这里你有一个 numpythonic 解决方案（这比明确地做一个循环要好得多）。

我使用滚动函数将位置中的数字+1 或-1 移动。另外一个"peak"被定义为局部最大值，前后数都小于中心值。

完整代码为：

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)

如果你绘制它，你会得到：

Answer 4

来自 `scipy.signal`

的 find_peaks 的解决方案

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()

结果图如下所示。

注意find_peaks有一个参数height，也就是我们这里所说的thresh。它还有一个名为 threshold 的参数，它正在做其他事情。

Documentation for find_peaks

Python 中的峰值检测算法

Peak detection algorithm in Python

python

function

detection

detect

来自 `scipy.signal`

Python 中的峰值检测算法

Peak detection algorithm in Python

python

function

detection

detect

来自 scipy.signal

来自 `scipy.signal`