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Detecting extreme values ​​in Python

· 2 min read
ひかり
ひかり
Main bloger

Detecting extrema in a signal.​

Generating a spurious signal as an example.​

  • 3 [Hz] signal + 0.01 [Hz] signal + noise
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from scipy import signal

tmp

Examining the properties of the signal.​

def acorr(df: pd.DataFrame, ra: int = 3, fs=100):
   x = np.correlate(df.Data.values, df.Data.values, mode='full')
   t = (np.arange(len(x)) - len(x) / 2 + 0.5) / fs
   x /= x.max()
   fig, ax = plt.subplots()
   ax.set_xlim(-ra, ra)
   ax.set_ylim(0, 1)
   ax.plot(t, x)
   ax.set_title('Autocorrelation')
   ax.grid(axis='x')
   ax.set_xticks(np.linspace(-ra, ra, 2 * ra + 1))
   plt.show()

acorr(df)

The main signal is 1/3 [Hz]. Therefore, a low-pass filter with a cutoff of 1/3 [Hz] is applied.

tmp

Applying a low-pass filter and detecting extrema.

If the extrema are not correctly detected even after applying a low-pass filter at 1/3 [Hz], the frequency is lowered.

tmp

fs = 10
lpf = 0.1
b, a = signal.butter(5, lpf / fs * 2, 'low')
df['Filter'] = signal.filtfilt(b, a, df.Data.values)
max_idx = signal.argrelextrema(df['Filter'].values, np.greater)[0]
min_idx = signal.argrelextrema(df['Filter'].values, np.less)[0]

df['max_index'] = False
df.iloc[max_idx[0], 2] = True
df['min_index'] = False
df.iloc[min_idx[0], 3] = True

fig, ax = plt.subplots()
df.plot(ax=ax)
ax.set_xlim(['00:00:00', '00:00:30'])
ax.scatter(
   df.loc[df['max_index'], ['Filter']].index, 
   df.loc[df['max_index'], ['Filter']], 
   color='tab:orange', 
   zorder=3)
ax.scatter(
   df.loc[df['min_index'], ['Filter']].index, 
   df.loc[df['min_index'], ['Filter']], 
   color='tab:green', 
   zorder=3)
plt.show()