Module wavelet.transforms.wavelet_transform
Discrete Wavelet and Inverse Transform implementation
Expand source code
"""Discrete Wavelet and Inverse Transform implementation"""
from wavelet.wavelets import getWaveletDefinition
class WaveletTransform:
"""
Class to run the selected wavelet and to perform the dwt & idwt
based on the wavelet filters
Attributes
----------
__wavelet__: object
object of the selected wavelet class
"""
def __init__(self, waveletName):
self.__wavelet__ = getWaveletDefinition(waveletName)
def dwt(self, arrTime, level):
"""
Discrete Wavelet Transform
Parameters
----------
arrTime : array_like
input array in Time domain
level : int
level to decompose
Returns
-------
array_like
output array in Frequency or the Hilbert domain
"""
arrHilbert = [0.] * level
# shrinking value 8 -> 4 -> 2
a = level >> 1
for i in range(a):
for j in range(self.__wavelet__.__motherWaveletLength__):
k = (i << 1) + j
# circulate the array if scale is higher
while k >= level:
k -= level
# approx & detail coefficient
arrHilbert[i] += arrTime[k] * self.__wavelet__.decompositionLowFilter[j]
arrHilbert[i + a] += arrTime[k] * self.__wavelet__.decompositionHighFilter[j]
return arrHilbert
def idwt(self, arrHilbert, level):
"""
Inverse Discrete Wavelet Transform
Parameters
----------
arrHilbert : array_like
input array in Frequency or the Hilbert domain
level : int
level to decompose
Returns
-------
array_like
output array in Time domain
"""
arrTime = [0.] * level
# shrinking value 8 -> 4 -> 2
a = level >> 1
for i in range(a):
for j in range(self.__wavelet__.__motherWaveletLength__):
k = (i << 1) + j
# circulating the array if scale is higher
while k >= level:
k -= level
# summing the approx & detail coefficient
arrTime[k] += (arrHilbert[i] * self.__wavelet__.reconstructionLowFilter[j] +
arrHilbert[i + a] * self.__wavelet__.reconstructionHighFilter[j])
return arrTimeClasses
class WaveletTransform (waveletName)-
Class to run the selected wavelet and to perform the dwt & idwt based on the wavelet filters
Attributes
__wavelet__:object- object of the selected wavelet class
Expand source code
class WaveletTransform: """ Class to run the selected wavelet and to perform the dwt & idwt based on the wavelet filters Attributes ---------- __wavelet__: object object of the selected wavelet class """ def __init__(self, waveletName): self.__wavelet__ = getWaveletDefinition(waveletName) def dwt(self, arrTime, level): """ Discrete Wavelet Transform Parameters ---------- arrTime : array_like input array in Time domain level : int level to decompose Returns ------- array_like output array in Frequency or the Hilbert domain """ arrHilbert = [0.] * level # shrinking value 8 -> 4 -> 2 a = level >> 1 for i in range(a): for j in range(self.__wavelet__.__motherWaveletLength__): k = (i << 1) + j # circulate the array if scale is higher while k >= level: k -= level # approx & detail coefficient arrHilbert[i] += arrTime[k] * self.__wavelet__.decompositionLowFilter[j] arrHilbert[i + a] += arrTime[k] * self.__wavelet__.decompositionHighFilter[j] return arrHilbert def idwt(self, arrHilbert, level): """ Inverse Discrete Wavelet Transform Parameters ---------- arrHilbert : array_like input array in Frequency or the Hilbert domain level : int level to decompose Returns ------- array_like output array in Time domain """ arrTime = [0.] * level # shrinking value 8 -> 4 -> 2 a = level >> 1 for i in range(a): for j in range(self.__wavelet__.__motherWaveletLength__): k = (i << 1) + j # circulating the array if scale is higher while k >= level: k -= level # summing the approx & detail coefficient arrTime[k] += (arrHilbert[i] * self.__wavelet__.reconstructionLowFilter[j] + arrHilbert[i + a] * self.__wavelet__.reconstructionHighFilter[j]) return arrTimeMethods
def dwt(self, arrTime, level)-
Discrete Wavelet Transform
Parameters
arrTime:array_like- input array in Time domain
level:int- level to decompose
Returns
array_like- output array in Frequency or the Hilbert domain
Expand source code
def dwt(self, arrTime, level): """ Discrete Wavelet Transform Parameters ---------- arrTime : array_like input array in Time domain level : int level to decompose Returns ------- array_like output array in Frequency or the Hilbert domain """ arrHilbert = [0.] * level # shrinking value 8 -> 4 -> 2 a = level >> 1 for i in range(a): for j in range(self.__wavelet__.__motherWaveletLength__): k = (i << 1) + j # circulate the array if scale is higher while k >= level: k -= level # approx & detail coefficient arrHilbert[i] += arrTime[k] * self.__wavelet__.decompositionLowFilter[j] arrHilbert[i + a] += arrTime[k] * self.__wavelet__.decompositionHighFilter[j] return arrHilbert def idwt(self, arrHilbert, level)-
Inverse Discrete Wavelet Transform
Parameters
arrHilbert:array_like- input array in Frequency or the Hilbert domain
level:int- level to decompose
Returns
array_like- output array in Time domain
Expand source code
def idwt(self, arrHilbert, level): """ Inverse Discrete Wavelet Transform Parameters ---------- arrHilbert : array_like input array in Frequency or the Hilbert domain level : int level to decompose Returns ------- array_like output array in Time domain """ arrTime = [0.] * level # shrinking value 8 -> 4 -> 2 a = level >> 1 for i in range(a): for j in range(self.__wavelet__.__motherWaveletLength__): k = (i << 1) + j # circulating the array if scale is higher while k >= level: k -= level # summing the approx & detail coefficient arrTime[k] += (arrHilbert[i] * self.__wavelet__.reconstructionLowFilter[j] + arrHilbert[i + a] * self.__wavelet__.reconstructionHighFilter[j]) return arrTime