Wavelet Analysis of Time Series Data in Python

I have data having 1440*8 and time in hour: The time repeats every 1440: Write python script to analyze the time series data using wavelate approach

To analyze time series data using the wavelet approach in Python, you can use the PyWavelets library, which provides tools for discrete wavelet transforms. Below is a Python script that demonstrates how to perform wavelet analysis on your time series data, assuming you have a 2D NumPy array with shape (1440, 8).

Prerequisites

Make sure you have the required libraries installed. You can install them using pip if you haven't already:

pip install numpy matplotlib pywavelets

Python Script

import numpy as np
import matplotlib.pyplot as plt
import pywt

# Generate synthetic data for demonstration (replace this with your actual data)
# Assuming your data is a 2D NumPy array with shape (1440, 8)
# For example, let's create a sine wave with noise
np.random.seed(0)
time = np.arange(1440)
data = np.array([np.sin(2 * np.pi * time / 1440) + np.random.normal(0, 0.1, 1440) for _ in range(8)])

# Function to perform wavelet transform and plot results
def wavelet_analysis(data):
    # Choose a wavelet
    wavelet = 'haar'  # You can choose other wavelets like 'db1', 'db2', 'sym2', etc.
    
    # Create a figure for plotting
    plt.figure(figsize=(12, 8))
    
    for i in range(data.shape[1]):
        # Perform discrete wavelet transform
        coeffs = pywt.wavedec(data[:, i], wavelet)
        
        # Plot the original signal
        plt.subplot(data.shape[1], 2, 2*i + 1)
        plt.plot(data[:, i])
        plt.title(f'Original Signal {i+1}')
        plt.xlabel('Time (minutes)')
        plt.ylabel('Amplitude')
        
        # Plot the wavelet coefficients
        plt.subplot(data.shape[1], 2, 2*i + 2)
        for j, coeff in enumerate(coeffs):
            plt.plot(coeff, label=f'Level {j}')
        plt.title(f'Wavelet Coefficients for Signal {i+1}')
        plt.xlabel('Coefficient Index')
        plt.ylabel('Coefficient Value')
        plt.legend()
    
    plt.tight_layout()
    plt.show()

# Perform wavelet analysis on the data
wavelet_analysis(data)

Explanation

1. Data Generation: The script generates synthetic data for demonstration purposes. Replace this part with your actual data loading mechanism.
2. Wavelet Analysis Function: The wavelet_analysis function performs the following:
   • It selects a wavelet (in this case, Haar wavelet).
   • It performs a discrete wavelet transform (DWT) on each of the 8 signals.
   • It plots the original signals and their corresponding wavelet coefficients.
3. Plotting: The results are visualized using Matplotlib, showing both the original signals and their wavelet coefficients.

Customization

• You can change the wavelet type by modifying the wavelet variable in the wavelet_analysis function.
• Adjust the plotting parameters as needed to fit your data and preferences.

This script provides a basic framework for wavelet analysis of time series data. You can expand upon it by adding more analysis, such as thresholding coefficients for noise reduction or reconstructing signals from selected coefficients.