Python中一维小波的能量

Question

I was wondering if there is an implementation for the Energy for 1-D wavelet in Python, the same as the Matlab '[Ea,Ed] = wenergy(C,L) '. I have tried to write one on my own but i am not sure of it: The formula is:

Where Dj is supposed the detail vector, and j = 1,2,...,ld and N1 is the data length at the decomposition level.

import json
import pywt
f=open('DataFile.txt','r')
D=json.load(f)
f.close()
#create the wavelet function
db1 = pywt.Wavelet('db13')
#calculate the number of necessary decompositions
NbrDecomp= pywt.dwt_max_level(len(D), db1)+1
#Initialize an empty list to receive the Detail and Approximation
Vector = [None] * NbrDecomp
#we use the Wavelet decomposition in the pywt module 
Vector = pywt.wavedec(D, db1)
#Now Vector = [Approxiamtion N, Details N, Details N-1,.....] 
#Where N would be the number of decompositions

According to the definition the energy at the level k is :

Energy(k)=np.sqrt(sum([x**2 for x in Vecktor[len(Vektor)-N-1-k]])/len(Vektor))

Was the implementation correct ?

Answer 1

You can simplify your code a little bit:

coeffs[len(coeffs) - k - 1]

can be rewritten as

coeffs[-k]

and you can do the squaring and summation as one NumPy operation (since you're using NumPy already)

def Energy(coeffs, k):
    return np.sqrt(np.sum(np.array(coeffs[-k]) ** 2)) / len(coeffs[-k])