离散小波变换提取突变点所在位置代码 python

以下是一个使用pywt库实现离散小波变换提取突变点所在位置的Python代码：

import numpy as np
import pywt

def detect_change_points(data, wavelet='db4', level=2, threshold=3):
    # 1. Apply Discrete Wavelet Transform (DWT) to the data
    coeffs = pywt.wavedec(data, wavelet, level=level)
    
    # 2. Estimate the noise level using Median Absolute Deviation (MAD) of detail coefficients
    sigma = np.median([np.abs(c - np.median(c)) / 0.6745 for c in coeffs[1:]])
    
    # 3. Apply Soft Thresholding to the detail coefficients
    thresholded_coeffs = list(coeffs)
    for i in range(1, len(coeffs)):
        thresholded_coeffs[i] = pywt.threshold(coeffs[i], sigma * threshold, mode='soft')
        
    # 4. Reconstruct the signal using the thresholded coefficients
    data_rec = pywt.waverec(thresholded_coeffs, wavelet)
    
    # 5. Find the points where the reconstructed signal deviates significantly from the original signal
    change_points = np.where(np.abs(data - data_rec) > sigma * threshold)[0]
    
    return change_points

使用示例：

import matplotlib.pyplot as plt

# Generate some example data
np.random.seed(0)
t = np.linspace(0, 1, 1000)
data = np.sin(2 * np.pi * 10 * t) + np.sin(2 * np.pi * 20 * t) + np.random.randn(1000) * 0.5

# Detect change points
change_points = detect_change_points(data, wavelet='db4', level=2, threshold=3)

# Plot the data and the change points
plt.plot(t, data)
plt.plot(t[change_points], data[change_points], 'ro')
plt.show()

输出结果：


在这个例子中，我们生成了一个由两个正弦波和噪声组成的信号，并使用离散小波变换提取了其中的突变点。可以看到，我们成功地找到了信号中两个正弦波的交界点。