Python | Fast Walsh Hadamard Transform

Fast Walsh Hadamard Transform, is an Hadamard ordered efficient algorithm to compute the Walsh Hadamard transform (WHT). Normal WHT computation has N = 2^m complexity but using FWHT 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.fwht( ) : It can perform Walsh Hadamard Transform (WHT). This method uses 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.

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

Returns : 
Fast Walsh Hadamard Transform Transform

Example #1 :

Python3

# import sympy 

from sympy import fwht
 
# sequence 

seq = [23, 

       56, 

       12, 

       555]
 
# hwht

transform = fwht(seq)

print ("Transform  : ", transform)

Output :

Transform  :  [646, -576, -488, 510]

Example #2 :

Python3

# import sympy 

from sympy import fwht
 
# sequence 

seq = [15, 21, 13, 44]
 
# hwht

transform = fwht(seq)

print ("Transform  : ", transform)

Output :

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

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