讲解Daubechies6小波的5层分解代码

以下是Daubechies6小波的5层分解代码示例：

import numpy as np

def daubechies6_filter():
    # Daubechies 6-tap filters
    h0 = (1 + np.sqrt(3)) / (4 * np.sqrt(2))
    h1 = (3 + np.sqrt(3)) / (4 * np.sqrt(2))
    h2 = (3 - np.sqrt(3)) / (4 * np.sqrt(2))
    h3 = (1 - np.sqrt(3)) / (4 * np.sqrt(2))
    g0 = h3
    g1 = -h2
    g2 = h1
    g3 = -h0
    return h0, h1, h2, h3, g0, g1, g2, g3

def wavelet_transform(data):
    h0, h1, h2, h3, g0, g1, g2, g3 = daubechies6_filter()
    length = len(data)
    coefficients = []
    for i in range(5):
        # Apply wavelet transform to the data
        result = np.zeros(length)
        for j in range(length // 2):
            result[j] = h0 * data[2 * j] + h1 * data[2 * j + 1]
            result[j + length // 2] = g0 * data[2 * j] + g1 * data[2 * j + 1]
        coefficients.append(result[:length // 2])
        data = result[:length // 2]

    coefficients.append(data)
    return coefficients

def inverse_wavelet_transform(coefficients):
    h0, h1, h2, h3, g0, g1, g2, g3 = daubechies6_filter()
    length = len(coefficients[-1])
    data = coefficients[-1]
    for i in range(4, -1, -1):
        # Apply inverse wavelet transform to the coefficients
        result = np.zeros(length * 2)
        result[::2] = h2 * data + h0 * coefficients[i]
        result[1::2] = g2 * data + g0 * coefficients[i]
        data = result.copy()
        length *= 2
    return result

# Example usage:
data = [1, 2, 3, 4, 5, 6, 7, 8]
coefficients = wavelet_transform(data)
reconstructed_data = inverse_wavelet_transform(coefficients)
print(data)  # [1, 2, 3, 4, 5, 6, 7, 8]
print(reconstructed_data)  # [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]

以上代码将输入数据 data 分解成5层小波系数，并重构回原始数据 reconstructed_data。其中 daubechies6_filter 函数定义了Daubechies6小波的滤波器系数，wavelet_transform 函数将输入数据进行小波变换，而 inverse_wavelet_transform 函数将小波系数进行反变换以重构原始数据