<div dir="ltr">I have my own code for FHT if you are interested</div><br><div class="gmail_quote"><div dir="ltr">On Thu, Mar 22, 2018 at 2:52 PM Chaman Agrawal <<a href="mailto:chaman.ag@gmail.com">chaman.ag@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div class="gmail_quote"><div dir="ltr"><p style="box-sizing:border-box;margin-bottom:16px;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;margin-top:0px">Issue #8590 <a href="https://github.com/scipy/scipy/issues/8590" target="_blank">https://github.com/scipy/scipy/issues/8590</a></p><p style="box-sizing:border-box;margin-bottom:16px;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;margin-top:0px">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.</p><h2 style="box-sizing:border-box;margin-top:24px;margin-bottom:16px;font-size:1.5em;font-weight:600;line-height:1.25;padding-bottom:0.3em;border-bottom:1px solid rgb(234,236,239);color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Fast Walsh–Hadamard transform</h2><p style="box-sizing:border-box;margin-top:0px;margin-bottom:16px;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">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.</p><h3 style="box-sizing:border-box;margin-top:24px;margin-bottom:16px;font-size:1.25em;font-weight:600;line-height:1.25;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Time Complexity:</h3><p style="box-sizing:border-box;margin-top:0px;margin-bottom:16px;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">O(nlogn) with Fast Walsh-Hadamard transform (FWHT)</p><h3 style="box-sizing:border-box;margin-top:24px;margin-bottom:16px;font-size:1.25em;font-weight:600;line-height:1.25;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Comparison with FFT:</h3><p style="box-sizing:border-box;margin-top:0px;margin-bottom:16px;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">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.</p><h3 style="box-sizing:border-box;margin-top:24px;margin-bottom:16px;font-size:1.25em;font-weight:600;line-height:1.25;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Some Usage examples:</h3><p style="box-sizing:border-box;margin-top:0px;color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol";font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;margin-bottom:0px">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.</p><br></div>
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