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Pustam | पुस्तम | পুস্তম🇳🇵The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. It decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. This is particularly useful in many fields, such as signal processing, physics, and engineering, because it allows for analysing the frequency characteristics of signals. The Fourier Transform provides a bridge between the time and frequency domains, enabling the analysis and manipulation of signals in more intuitive and computationally efficient ways. The result of applying a Fourier Transform is often represented as a spectrum, showing how much of each frequency is present in the original signal.\[\Large\boxed{\boxed{\widehat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,\mathrm dx, \quad \forall\xi \in \mathbb{R}.}}\]Inverse Fourier Transform: \[\Large\boxed{\boxed{ f(x) = \int_{-\infty}^{\infty} \widehat f(\xi)\ e^{i 2 \pi \xi x}\,\mathrm d\xi,\quad \forall x \in \mathbb R.}}\] The equation allows us to listen to mp3s today. Digital Music Couldn’t Exist Without the Fourier Transform: <a href="http://bit.ly/22kbNfi" rel="nofollow noopener noreferrer" translate="no" target="_blank">http://bit.ly/22kbNfi</a><a href="https://mathstodon.xyz/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> <a href="https://mathstodon.xyz/tags/FourierTransform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FourierTransform</a> <a href="https://mathstodon.xyz/tags/Transform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Transform</a> <a href="https://mathstodon.xyz/tags/Time" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Time</a> <a href="https://mathstodon.xyz/tags/Frequency" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Frequency</a> <a href="https://mathstodon.xyz/tags/Space" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Space</a> <a href="https://mathstodon.xyz/tags/TimeDomain" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#TimeDomain</a> <a href="https://mathstodon.xyz/tags/FrequencyDomain" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FrequencyDomain</a> <a href="https://mathstodon.xyz/tags/Wavenumber" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Wavenumber</a> <a href="https://mathstodon.xyz/tags/WavenumberDomain" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#WavenumberDomain</a> <a href="https://mathstodon.xyz/tags/Function" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Function</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/JosephFourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JosephFourier</a> <a href="https://mathstodon.xyz/tags/Signal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Signal</a> <a href="https://mathstodon.xyz/tags/Signals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Signals</a> <a href="https://mathstodon.xyz/tags/FT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FT</a> <a href="https://mathstodon.xyz/tags/IFT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IFT</a> <a href="https://mathstodon.xyz/tags/DFT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DFT</a> <a href="https://mathstodon.xyz/tags/FFT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FFT</a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physics</a> <a href="https://mathstodon.xyz/tags/SignalProcessing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SignalProcessing</a> <a href="https://mathstodon.xyz/tags/Engineering" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Engineering</a> <a href="https://mathstodon.xyz/tags/Analysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Analysis</a> <a href="https://mathstodon.xyz/tags/Computing" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Computing</a> <a href="https://mathstodon.xyz/tags/Computation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Computation</a> <a href="https://mathstodon.xyz/tags/Operation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Operation</a> <a href="https://mathstodon.xyz/tags/ComplexSignal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ComplexSignal</a> <a href="https://mathstodon.xyz/tags/Sinusoidal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sinusoidal</a> <a href="https://mathstodon.xyz/tags/Amplitude" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Amplitude</a> <a href="https://mathstodon.xyz/tags/Phase" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Phase</a> <a href="https://mathstodon.xyz/tags/Spectra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Spectra</a> <a href="https://mathstodon.xyz/tags/Spectrum" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Spectrum</a> <a href="https://mathstodon.xyz/tags/Pustam" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pustam</a> <a href="https://mathstodon.xyz/tags/Raut" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Raut</a> <a href="https://mathstodon.xyz/tags/PustamRaut" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PustamRaut</a> <a href="https://mathstodon.xyz/tags/EGR" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EGR</a> <a href="https://mathstodon.xyz/tags/Mathstodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathstodon</a> <a href="https://mathstodon.xyz/tags/Mastodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mastodon</a> <a href="https://mathstodon.xyz/tags/GeoFlow" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GeoFlow</a> <a href="https://mathstodon.xyz/tags/SpectralMethod" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SpectralMethod</a>

Paul Giulan<a href="https://federate.social/tags/Humanoid" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Humanoid</a> <a href="https://federate.social/tags/robot" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#robot</a> comparison<a href="https://federate.social/tags/Canada" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Canada</a> <a href="https://federate.social/tags/China" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#China</a> <a href="https://federate.social/tags/Singapore" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Singapore</a> <a href="https://federate.social/tags/USA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#USA</a> <a href="https://federate.social/tags/Agility" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Agility</a> <a href="https://federate.social/tags/BostonDynamics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BostonDynamics</a> <a href="https://federate.social/tags/Figure" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Figure</a> <a href="https://federate.social/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> <a href="https://federate.social/tags/Sanctuary" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Sanctuary</a> <a href="https://federate.social/tags/Tesla" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Tesla</a> <a href="https://federate.social/tags/Unitree" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Unitree</a> <a href="https://federate.social/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a> <a href="https://federate.social/tags/ArtificialIntelligence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ArtificialIntelligence</a> <a href="https://federate.social/tags/LLM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LLM</a> <a href="https://federate.social/tags/DataViz" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DataViz</a> <a href="https://federate.social/tags/visualization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#visualization</a> <a href="https://federate.social/tags/humanoid" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#humanoid</a> <a href="https://federate.social/tags/robots" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#robots</a>

bazkie, lanparty callgirl"Watching Neural Networks Learn" by Emergent GardenCool video explaining NNs without using too much complicated maths, but instead with cool visuals.<a href="https://www.youtube.com/watch?v=TkwXa7Cvfr8" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.youtube.com/watch?v=TkwXa7Cvfr8</a><a href="https://beige.party/tags/NeuralNetworks" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NeuralNetworks</a> <a href="https://beige.party/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a>

∞ 𝕁uan ℂarlosHomer Simpson's Orbit <a href="https://youtu.be/slfS7j_7L6s" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://youtu.be/slfS7j_7L6s</a> <a href="https://mathstodon.xyz/tags/discrete" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#discrete</a> <a href="https://mathstodon.xyz/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> <a href="https://mathstodon.xyz/tags/transform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#transform</a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a>

amen zwa, esq.The <a href="https://mathstodon.xyz/tags/CooleyTukey" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CooleyTukey</a> <a href="https://mathstodon.xyz/tags/FFT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FFT</a> is one of the foundational algorithms that powers the 21st Century world. Their paper, "An Algorithm for the Machine Calculation of Complex <a href="https://mathstodon.xyz/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> Series" (1965), has been read by millions of <a href="https://mathstodon.xyz/tags/EE" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EE</a> students, round the world, for 60 years.<a href="https://web.stanford.edu/class/cme324/classics/cooley-tukey.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://web.stanford.edu/class/cme324/classics/cooley-tukey.pdf</a>But to non-EEs (say, <a href="https://mathstodon.xyz/tags/CS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CS</a> students), I believe Cooley's reminiscence, "The Re-Discovery of the Fast Fourier Transform Algorithm" (1987), is a gentler introduction.<a href="https://carmamaths.org/resources/jon/Preprints/Talks/CARMA-CE/FFT.pdf" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://carmamaths.org/resources/jon/Preprints/Talks/CARMA-CE/FFT.pdf</a>

Ele Willoughby, PhDNow I’m adding sinusoids! Sometimes people ask me to make portraits of scientists that I have long considered portraying. So when asked to make mathematician and physicist Joseph Fourier’s portrait I already had an idea about trying to show how Fourier analysis taught us we can make any shape- even his own outline- by summing sinusoids. I hadn’t completely worked out how to tell this story in a print, … 🧵1/n<a href="https://spore.social/tags/linocut" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#linocut</a> <a href="https://spore.social/tags/printmaking" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#printmaking</a> <a href="https://spore.social/tags/sciart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sciart</a> <a href="https://spore.social/tags/mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathart</a> <a href="https://spore.social/tags/histSci" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#histSci</a> <a href="https://spore.social/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> <a href="https://spore.social/tags/wip" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#wip</a> <a href="https://spore.social/tags/MastoArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MastoArt</a>

Spektrum (inoffiziell)Manon Bischoff teilt ihre Faszination für die Mathematik in 62 unterhaltsamen und informativen Beiträgen – zum Satz des Pythagoras ebenso wie zum »Sandwich-Problem«. Eine RezensionMathematik ist keine garstige Fremdsprache, sondern kann faszinierend, zugänglich und unterhaltsam sein. Das belegt dieses Buch eindrücklich. Eine Rezension (Rezension zu Die fabelhafte Welt der Mathematik von Manon Bischoff)<a href="https://anonsys.net/search?tag=Mathematik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematik</a> <a href="https://anonsys.net/search?tag=Geometrie" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Geometrie</a> <a href="https://anonsys.net/search?tag=Pi" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pi</a> <a href="https://anonsys.net/search?tag=Zahlen" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Zahlen</a> <a href="https://anonsys.net/search?tag=Unendlich" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Unendlich</a> <a href="https://anonsys.net/search?tag=Statistik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Statistik</a> <a href="https://anonsys.net/search?tag=Gleichung" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Gleichung</a> <a href="https://anonsys.net/search?tag=Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> <a href="https://anonsys.net/search?tag=Pythagoras" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Pythagoras</a> <a href="https://anonsys.net/search?tag=ITTech" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ITTech</a> <a href="https://anonsys.net/search?tag=Kultur" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Kultur</a> <a href="https://anonsys.net/search?tag=Physik" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Physik</a> <a href="https://www.spektrum.de/rezension/buchkritik-zu-die-fabelhafte-welt-der-mathematik/2216149" rel="nofollow noopener noreferrer" target="_blank">»Die fabelhafte Welt der Mathematik«: Ein Leben ohne Mathematik ist möglich, aber nicht wünschenswert</a>

∞ 𝕁uan ℂarlos<a href="https://www.dynamicmath.xyz/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.dynamicmath.xyz/</a><a href="https://mathstodon.xyz/tags/opensource" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#opensource</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/visualization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#visualization</a> <a href="https://mathstodon.xyz/tags/complex" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#complex</a> <a href="https://mathstodon.xyz/tags/analysis" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#analysis</a> <a href="https://mathstodon.xyz/tags/fractals" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fractals</a> <a href="https://mathstodon.xyz/tags/modelling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#modelling</a> <a href="https://mathstodon.xyz/tags/differential" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#differential</a> <a href="https://mathstodon.xyz/tags/equations" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#equations</a> <a href="https://mathstodon.xyz/tags/mathematicalArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematicalArt</a> <a href="https://mathstodon.xyz/tags/calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#calculus</a> <a href="https://mathstodon.xyz/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> <a href="https://mathstodon.xyz/tags/fouriertransform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fouriertransform</a>

Bifurkatus 🎭<a href="https://c.im/@etcetera" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@etcetera</a> Did someone try use <a href="https://dresden.network/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> for vector graphics compression yet?<a href="https://dresden.network/tags/imagecompression" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#imagecompression</a> <a href="https://dresden.network/tags/osm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#osm</a> <a href="https://dresden.network/tags/vectorart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#vectorart</a> <a href="https://dresden.network/tags/svg" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#svg</a>

dr 🛠️🛰️📡🎧:blobfoxcomputer:Maddening. I spent far too long today browsing <a href="https://hachyderm.io/tags/nerd" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nerd</a> <a href="https://hachyderm.io/tags/stickers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#stickers</a> for my water bottle. Just on an off chance, I tried "<a href="https://hachyderm.io/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a>" and found a really neat one!The <a href="https://hachyderm.io/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> is wrong. It shows the sum as being a square wave but the actual series shown would be a sawtooth.

⏣ Prof. Oliver JonesA new CSI style <a href="https://fosstodon.org/tags/forensic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#forensic</a> chemistry paper to start the week. Hand-held analytical instruments such as <a href="https://fosstodon.org/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> transform infrared and <a href="https://fosstodon.org/tags/Raman" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Raman</a> <a href="https://fosstodon.org/tags/spectroscopy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#spectroscopy</a> are useful for taking samples in the field but lack sensitivity. We show we can use <a href="https://fosstodon.org/tags/datafusion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#datafusion</a> to combine FTIR and Raman data to classify the method used to make the starting compounds needed to make the drug <a href="https://fosstodon.org/tags/fentanyl" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fentanyl</a>. Free access via <a href="https://authors.elsevier.com/c/1geA68nCdJ744-" rel="nofollow noopener noreferrer" target="_blank">https://authors.elsevier.com/c/1geA68nCdJ744-</a><a href="https://fosstodon.org/tags/ozchem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ozchem</a> <a href="https://fosstodon.org/tags/forensics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#forensics</a> <a href="https://fosstodon.org/tags/science" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#science</a> <a href="https://fosstodon.org/tags/data" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#data</a>

dr 🛠️🛰️📡🎧:blobfoxcomputer:<a href="https://fediscience.org/@drdrowland" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@drdrowland</a> Will do. Meanwhile, I remember this bio. I want to try this <a href="https://hachyderm.io/tags/rhythm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#rhythm</a> <a href="https://hachyderm.io/tags/game" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#game</a> that teaches <a href="https://hachyderm.io/tags/conga" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#conga</a>, <a href="https://hachyderm.io/tags/python" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#python</a> and <a href="https://hachyderm.io/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> transforms

Jens Hannemann<a href="https://mathstodon.xyz/@anton_hilado" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@anton_hilado</a> For me, that's without a doubt the Fourier-Slice Theorem:<a href="https://en.wikipedia.org/wiki/Projection-slice_theorem" rel="nofollow noopener noreferrer" target="_blank">https://en.wikipedia.org/wiki/Projection-slice_theorem</a>It's the basis of medical CT, but more importantly, it's just so darn fundamental and - yes - beautiful, driving home the point that the spatial and spectral domain are completely equivalent representations of information.<a href="https://mastodon.online/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mastodon.online/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mastodon.online/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> <a href="https://mastodon.online/tags/Engineering" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Engineering</a> <a href="https://mastodon.online/tags/MedicalImaging" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MedicalImaging</a>

New Submissions to TMLRFourier Sensitivity and Regularization of Computer Vision Models<a href="https://openreview.net/forum?id=VmTYgjYloM" rel="nofollow noopener noreferrer" target="_blank">https://openreview.net/forum?id=VmTYgjYloM</a><a href="https://sigmoid.social/tags/regularization" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#regularization</a> <a href="https://sigmoid.social/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> <a href="https://sigmoid.social/tags/robustness" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#robustness</a>

Canaima GNU/Linux<a href="https://mstdn.social/tags/UnDiaComoHoy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#UnDiaComoHoy</a> nació la matemática Maryna Viazovska.Profesora de teoría de números.Segunda mujer en recibir la <a href="https://mstdn.social/tags/MedallaFields" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MedallaFields</a> por su trabajo sobre el empaquetamiento de esferas en la dimensión 8 y sus contribuciones a los problemas de interpolación en el análisis de <a href="https://mstdn.social/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a><a href="https://mstdn.social/tags/MujeresSTEM" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MujeresSTEM</a>

Club de TéléMatique :verified:How I over-engineered a Fast Fourier Transform for Arduino: <a href="https://klafyvel.me/blog/articles/fft-arduino/" rel="nofollow noopener noreferrer" target="_blank">https://klafyvel.me/blog/articles/fft-arduino/</a> <a href="https://mstdn.social/tags/arduino" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#arduino</a> <a href="https://mstdn.social/tags/FFT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FFT</a> <a href="https://mstdn.social/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a>

Stephen GruppettaThere's a lot more to say. If you've found the posts above intriguing and you're interested to find out more about how **any** image can be decomposed and reconstructed from nothing other than sines and cosines……and you want to go through a step-by-step tutorial to write the <a href="https://mas.to/tags/Python" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Python</a> code to create this <a href="https://mas.to/tags/Fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Fourier</a> decomposition of images, you can read this article:Code uses <a href="https://mas.to/tags/Numpy" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Numpy</a> and <a href="https://mas.to/tags/Matplotlib" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Matplotlib</a>, of course (<a href="https://vis.social/@matplotlib" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@matplotlib</a>)/13<a href="https://mas.to/tags/Coding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Coding</a> <a href="https://mas.to/tags/Programming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Programming</a> <a href="https://mas.to/tags/FourierTransform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FourierTransform</a> <a href="https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/" rel="nofollow noopener noreferrer" target="_blank">https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/</a>

∞ 𝕁uan ℂarlos:) 🐘 <a href="https://mathstodon.xyz/tags/epicylces" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#epicylces</a> <a href="https://mathstodon.xyz/tags/curves" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#curves</a> <a href="https://mathstodon.xyz/tags/discrete" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#discrete</a> <a href="https://mathstodon.xyz/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> <a href="https://mathstodon.xyz/tags/transform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#transform</a>

Brian BeachOnce in a while, <a href="https://qoto.org/tags/veritasium" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#veritasium</a> creates a video that is stunningly good. This one on <a href="https://qoto.org/tags/FFT" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FFT</a> and <a href="https://qoto.org/tags/nuclear" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#nuclear</a> <a href="https://qoto.org/tags/disarmament" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#disarmament</a> was one.FFTs are something I wish I'd learned in school, and have never taken the time to really learn. This video was the best overview I've seen yet of <a href="https://qoto.org/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> transforms. And it also covers the application of FFTs to nuclear treaties, as well as a connection to <a href="https://qoto.org/tags/Gauss" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Gauss</a> I'd never heard before.<a href="https://www.youtube.com/watch?v=nmgFG7PUHfo" rel="nofollow noopener noreferrer" target="_blank">https://www.youtube.com/watch?v=nmgFG7PUHfo</a>

Stephen GruppettaThere's a lot more than can fit in a single thread.If you want to read more detail, and go through the step-by-step writing of the code to decompose & recostruct *any* image, read full article here: <a href="https://qoto.org/tags/coding" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#coding</a> <a href="https://qoto.org/tags/2dfourierimages" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#2dfourierimages</a> <a href="https://qoto.org/tags/2dfouriertransform" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#2dfouriertransform</a> <a href="https://qoto.org/tags/fourier" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fourier</a> /16<a href="https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/" rel="nofollow noopener noreferrer" target="_blank">https://thepythoncodingbook.com/2021/08/30/2d-fourier-transform-in-python-and-fourier-synthesis-of-images/</a>

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