离散小波变换 python_CDF 9/7离散小波变换（卷积）

实际上，我自己解决了这个问题，通过比较系数，然后重建，与这个提升实现的代码：

基本上，我

1）使边界条件对称，而不是周期性的

2）必须以一定的方式抵消卷积（和上采样）以使其对齐。在

下面是代码，以防其他人遇到问题。我觉得这仍然过于复杂化了，特别是因为它在任何地方都没有真正的文档记录，但至少它是有效的。这也包括我用来对照那个参考进行测试的“开关”，我必须修改Haar小波使其工作。在import random

import math

length = int()

array = list()

row = list()

scaleCoefficients = list()

waveletCoefficients = list()

reconstruction = list()

switch = False

def upsample1(lst, index):

if (index % 2 == 0):

return lst[index/2]

else:

return 0.0

def upsample2(lst, index):

if (index % 2 == 0):

return 0.0

else:

return lst[index/2]

## Generate a random list of floating point numbers

if (not switch):

length = 128

for i in range(length):

array.append(random.random())

else:

length = 32

for i in range(32):

array.append(5.0+i+.4*i*i-.02*i*i*i)

## First Part Just Calculates the Filters

## CDF 9/7 Wavelet

DWTAnalysisLowpass = [.026749, -.016864, -.078223, .266864, .602949, .266864, -.078223, -.016864, .026749]

for i in range(len(DWTAnalysisLowpass)):

DWTAnalysisLowpass[i] = math.sqrt(2.0) * DWTAnalysisLowpass[i]

DWTAnalysisHighpass = [.091272, -.057544, -0.591272, 1.115087, -.591272, -.057544, .091272]

for i in range(len(DWTAnalysisHighpass)):

DWTAnalysisHighpass[i] = DWTAnalysisHighpass[i]/math.sqrt(2.0)

DWTSynthesisLowpass = [-.091272, -.057544, 0.591272, 1.115087, .591272, -.057544, -.091272]

for i in range(len(DWTSynthesisLowpass)):

DWTSynthesisLowpass[i] = DWTSynthesisLowpass[i]/math.sqrt(2.0)

DWTSynthesisHighpass = [.026749, .016864, -.078223, -.266864, .602949, -.266864, -.078223, .016864, .026749]

for i in range(len(DWTSynthesisHighpass)):

DWTSynthesisHighpass[i] = math.sqrt(2.0) * DWTSynthesisHighpass[i]

## Haar Wavelet

## c = 1.0/math.sqrt(2)

## DWTAnalysisLowpass = [c,c]

## DWTAnalysisHighpass = [c, -c]

## DWTSynthesisLowpass = [-c, c]

## DWTSynthesisHighpass = [c, c]

# Do the forward transform. We can skip every other sample since they would

# be removed in the downsampling anyway

for i in range(0,length,2):

newVal = 0.0

## Convolve the next j elements by the low-pass analysis filter

for j in range(len(DWTAnalysisLowpass)):

index = i + j - len(DWTAnalysisLowpass)/2

if(index >= length):

index = 2*length - index - 2

elif (index < 0):

index = -index

newVal = newVal + array[index]*DWTAnalysisLowpass[j]

# append the new value to the list of scale coefficients

scaleCoefficients.append(newVal)

newVal = 0.0

# Convolve the next j elements by the high-pass analysis filter

for j in range(len(DWTAnalysisHighpass)):

index = i + j - len(DWTAnalysisHighpass)/2 + 1

if(index >= length):

index = 2*length - index - 2

elif (index < 0):

index = -index

newVal = newVal + array[index]*DWTAnalysisHighpass[j]

# append the new value to the list of wavelet coefficients

waveletCoefficients.append(newVal)

# Do the inverse transform

for i in range(length):

newVal = 0.0

# convolve the upsampled wavelet coefficients with the high-pass synthesis filter

for j in range(len(DWTSynthesisHighpass)):

index = i + j - len(DWTSynthesisHighpass)/2

if(index >= length):

index = 2*length - index - 2

elif (index < 0):

index = -index

newVal = newVal + upsample2(waveletCoefficients, index)*DWTSynthesisHighpass[j]

# convolve the upsampled scale coefficients with the low-pass synthesis filter, and

# add it to the previous convolution

for j in range(len(DWTSynthesisLowpass)):

index = i + j - len(DWTSynthesisLowpass)/2

if(index >= length):

index = 2*length - index - 2

elif (index < 0):

index = -index

newVal = newVal + upsample1(scaleCoefficients, index)*DWTSynthesisLowpass[j]

reconstruction.append(newVal)

print ("Sums: ")

print sum(reconstruction)

print sum(array)

print ("Original Signal: ")

print array

if (not switch):

print ("Wavelet Coefficients: ")

for i in range(len(scaleCoefficients)):

print ("sc[" + str(i) + "]: " + str(scaleCoefficients[i]))

for i in range(len(waveletCoefficients)):

print ("wc[" + str(i) + "]: " + str(waveletCoefficients[i]))

print ("Reconstruction: ")

print reconstruction

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离散小波变换 python_CDF 9/7离散小波变换（卷积）

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