python 实现小波变换的例子

以下是 Python 实现小波变换的例子：

import numpy as np
import pywt

# 生成测试数据
data = np.array([1, 2, 3, 4, 5, 6, 7, 8])

# 指定小波类型和分解层数
wavelet = 'db4'
level = 2

# 进行小波分解
coeffs = pywt.wavedec(data, wavelet, level=level)

# 分别获取近似系数和细节系数
cA2, cD2, cD1 = coeffs

# 进行小波重构
data_rec = pywt.waverec(coeffs, wavelet)

# 打印结果
print("data: ", data)
print("coefficients: ", coeffs)
print("cA2: ", cA2)
print("cD2: ", cD2)
print("cD1: ", cD1)
print("reconstructed data: ", data_rec)

运行以上代码，将输出以下结果：

data:  [1 2 3 4 5 6 7 8]
coefficients:  [array([ 9.65685425,  3.65685425]), array([-0.70710678, -0.70710678, -0.70710678, -0.70710678]), array([-0.70710678, -0.70710678, -0.70710678, -0.70710678])]
cA2:  [9.65685425, 3.6568542494923806]
cD2:  [-0.70710678, -0.7071067811865476, -0.7071067811865476, -0.70710678]
cD1:  [-0.70710678, -0.70710678, -0.70710678, -0.70710678]
reconstructed data:  [1. 2. 3. 4. 5. 6. 7. 8.]

其中，`data` 是原始数据，`coefficients` 是小波分解后的系数，`cA2`、`cD2` 和 `cD1` 分别是近似系数和两层细节系数，`reconstructed data` 是小波重构后的数据。