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# Python | Inverse Fast Walsh Hadamard Transformation

• Last Updated : 26 Aug, 2019

## 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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