# Python | Inverse Fast Walsh Hadamard Transformation

• Last Updated : 19 May, 2022

## 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 = 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 ```

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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