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

[Ralf Gommers]

On Thu, Mar 22, 2018 at 12:39 PM, Chaman Agrawal <chaman.ag at gmail.com>
wrote:

> Hello,
>

Hi Chaman, your email client seems to be misconfigured, you're starting new
threads. Can you please have a look at changing that?

Cheers,
Ralf


> Thanks, please send the link ,it would be good to have multiple references.
>
> However the important part is where to implement this ,in fftpack or
> signal as Ralf Gommers <https://github.com/rgommers> mentioned in the
> issue page.
>
> Cheers,
> Chaman
> 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 <https://mail.python.org/mailman/listinfo/scipy-dev>> wrote:
>
> >* Issue #8590 https://github.com/scipy/scipy/issues/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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