Python | Inverse Fast Walsh Hadamard Transformation

Inverse Fast Walsh Hadamard Transform

It is an Hadamard ordered efficient algorithm to compute the inverse Walsh Hadamard transform (WHT). Normal WHT computation has N = 2^m 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

Example #1 :

Python3

# 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 :

Python3

# 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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Python