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Python | Inverse Fast Walsh Hadamard Transformation

  • Last Updated : 26 Aug, 2019
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Inverse Fast Walsh Hadamard Transform

It is an Hadamard ordered efiicient algorithm to compute the inverse Walsh Hadamard transform (WHT). Normal WHT computation has N = 2m complexity but using IFWHT reduces the computation to O(n2). The FWHT requires O(n logn) additions and subtraction operations. It is a divide and conquer algorithm which breaks down the WHT recursively.

sympy.discrete.transforms.ifwht( ) :

It can perform Inverse Walsh Hadamard Transform (WHT). This method is based on Hadamard sequence ordering. Automatically the sequence is padded with zero to the right because the radix-2 FWHT requires the sample point number as a power of 2.


Syntax: 
sympy.discrete.transforms.ifwht()

Parameters : 
-> seq : [iterable] sequence on which IWHT is to be applied.

Returns : 
Coefficient of Inverse Fast Walsh Hadamard Transform Transform

Example #1 :




# import sympy 
from sympy import ifwht
  
# sequence 
seq = [15, 21, 13, 44]
  
# ifwht
transform = ifwht(seq)
print ("Transform  : ", transform)

Output :

Transform  :  [93/4, -37/4, -21/4, 25/4]



Example #2 :




# import sympy 
from sympy import ifwht
  
# sequence 
seq = [23
       56
       12
       555]
  
# ifwht
transform = ifwht(seq)
print ("Transform  : ", transform)

Output :

Transform  :  [323/2, -144, -122, 255/2]

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