get Pre-whitening signal by python

Pre-whitening is a technique used in signal processing to remove the spectral correlation of a signal, thus making it easier to analyze or model. Here is an example of how to pre-whiten a signal using Python and the NumPy library.

First, let's import the necessary libraries:

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import lfilter, butter

Next, let's generate a simple signal consisting of two sinusoids with different frequencies and amplitudes:

fs = 1000  # Sampling rate in Hz
t = np.arange(0, 1, 1/fs)  # Time vector from 0 to 1 second
n = len(t)  # Number of samples
f1 = 50  # First sinusoid frequency in Hz
f2 = 200  # Second sinusoid frequency in Hz
A1 = 1  # First sinusoid amplitude
A2 = 0.5  # Second sinusoid amplitude
x = A1*np.sin(2*np.pi*f1*t) + A2*np.sin(2*np.pi*f2*t)  # Signal

We can plot the signal to visualize it:

plt.plot(t, x)
plt.xlabel('Time (s)')
plt.ylabel('Amplitude')
plt.show()


Now we can pre-whiten the signal using a first-order Butterworth high-pass filter with a cutoff frequency of 10 Hz. This will remove the low-frequency components of the signal and leave us with a white noise signal:

f_cutoff = 10  # Cutoff frequency in Hz
b, a = butter(1, f_cutoff/(fs/2), btype='highpass')  # High-pass filter coefficients
x_filt = lfilter(b, a, x)  # Apply filter to signal

We can plot the filtered signal to visualize it:

plt.plot(t, x_filt)
plt.xlabel('Time (s)')
plt.ylabel('Amplitude')
plt.show()


As you can see, the pre-whitened signal has a flat spectral density, which means that its power is uniformly distributed across all frequencies. This makes it easier to analyze or model the signal without being biased by its spectral correlation.