[SciPy-Dev] Fast Walsh–Hadamard transform for SciPy ?

[Neal Becker]

I have my own code for FHT if you are interested

On Thu, Mar 22, 2018 at 2:52 PM Chaman Agrawal <chaman.ag at gmail.com> wrote:

> Issue #8590 https://github.com/scipy/scipy/issues/8590
>
> Currently there is no implementation of Fast Walsh–Hadamard transform in
> SciPy. Although it seems that FWHT is not as general as FFT but it is
> pretty ubiquitous ,it is there is other maths and science softwares like
> MATLAB etc. .I would like to contribute towards it. Following are the
> details about it.
> Fast Walsh–Hadamard transform
>
> Hadamard transform is an example of a generalized class of Fourier
> transforms. It performs an orthogonal, symmetric, involutive, linear
> operation on 2^(m) numbers. It is equivalent to a multidimensional DFT.
> Time Complexity:
>
> O(nlogn) with Fast Walsh-Hadamard transform (FWHT)
> Comparison with FFT:
>
> FWHT is very useful for reducing bandwidth storage requirements and
> spread-spectrum analysis. Compared to the FFT, the FWHT requires less
> storage space and is faster to calculate because it uses only real
> additions and subtractions, while the FFT requires complex values. The FWHT
> is able to represent signals with sharp discontinuities more accurately
> using fewer coefficients than the FFT.
> Some Usage examples:
>
> The Hadamard transform is used in data encryption, as well as many signal
> processing and data compression algorithms, such as JPEG XR and MPEG-4 AVC.
> It is also a crucial part of Grover's algorithm and Shor's algorithm in
> quantum computing. The Hadamard transform is also applied in scientific
> methods such as NMR, mass spectroscopy and crystallography.
>
>
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