In this blog post, we will explore the Morlet 웨이블릿 (wavelet) in Python using the Scipy library. Wavelets are mathematical functions that analyze signals and images by decomposing them into different frequency components. The Morlet wavelet is particularly useful for analyzing time-frequency structures in continuous signals.

Prerequisites

Make sure you have Python installed on your system, along with the Scipy library. You can install Scipy using pip:

pip install scipy

Understanding the Morlet Wavelet

The Morlet wavelet is a complex wavelet that resembles a Gaussian windowed sinusoid. It consists of a complex sinusoidal wave multiplied by a Gaussian window function. This wavelet is commonly used in analysis techniques such as time-frequency analysis and feature extraction from signals.

Using Scipy to Generate Morlet Wavelets

1. Import the necessary libraries:

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

1. Generate a Morlet wavelet with a specific frequency and width:

def generate_morlet_wavelet(freq, width, sampling_rate):
    time = np.arange(-width * 2, width * 2, 1/sampling_rate)
    wavelet = np.exp(2j * np.pi * freq * time) * np.exp(-time**2 / (2 * width**2))
    return wavelet

1. Plot the generated wavelet:

def plot_wavelet(time, wavelet):
    plt.figure()
    plt.plot(time, np.real(wavelet), label='Real part')
    plt.plot(time, np.imag(wavelet), label='Imaginary part')
    plt.xlabel('Time')
    plt.ylabel('Amplitude')
    plt.title('Morlet Wavelet')
    plt.legend()
    plt.show()

1. Generate and plot a Morlet wavelet with a frequency of 10 Hz and a width of 5:

sampling_rate = 1000  # Change this according to your requirement
freq = 10
width = 5
wavelet = generate_morlet_wavelet(freq, width, sampling_rate)
time = np.arange(-width * 2, width * 2, 1/sampling_rate)
plot_wavelet(time, wavelet)

Conclusion

In this blog post, we discussed the Morlet wavelet and how to generate it in Python using the Scipy library. The Morlet wavelet is a powerful tool for analyzing time-frequency structures in continuous signals. By understanding and utilizing this wavelet, you can extract valuable information from various types of data.