Discrete transforms | FFT algorithms

Cyclotomic fast Fourier transform

The cyclotomic fast Fourier transform is a type of fast Fourier transform algorithm over finite fields. This algorithm first decomposes a DFT into several circular convolutions, and then derives the DFT results from the circular convolution results. When applied to a DFT over , this algorithm has a very low multiplicative complexity. In practice, since there usually exist efficient algorithms for circular convolutions with specific lengths, this algorithm is very efficient. (Wikipedia).

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The Fast Fourier Transform (FFT)

Here I introduce the Fast Fourier Transform (FFT), which is how we compute the Fourier Transform on a computer. The FFT is one of the most important algorithms of all time. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow Chapter

From playlist Fourier

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Fourier Transforms: Fast Fourier Transform, Part 3

Data Science for Biologists Fourier Transforms: Fast Fourier Transform Part 3 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

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Math 139 Fourier Analysis Lecture 29: Finite Fourier Analysis; Fast Fourier Transform

Fourier coefficients of continuous functions on Z(N) (group of N-th roots of unity); Fourier inversion; Parseval-Plancherel formulae. Fast Fourier transform: how to best calculate the Fourier coefficients.

From playlist Course 8: Fourier Analysis

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Chandrashekhar Khare, Serre's conjecture and computational aspects of the Langlands program

VaNTAGe Seminar, April 5, 2022 License: CC-BY-NC-SA Some relevant links: Edixhoven-Couveignes-de Jong-Merkl-Bosman: https://arxiv.org/abs/math/0605244 Ramanujan's 1916 paper: http://ramanujan.sirinudi.org/Volumes/published/ram18.pdf Delta's home page in the LMFDB: https://www.lmfdb.org/

From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)

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Introduction to the z-Transform

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor

From playlist The z-Transform

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The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?

In this video, we take a look at one of the most beautiful algorithms ever created: the Fast Fourier Transform (FFT). This is a tricky algorithm to understand so we take a look at it in a context that we are all familiar with: polynomial multiplication. You will see how the core ideas of t

From playlist Fourier

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Adeline Roux-Langlois : Using structured variants in lattice-based cryptography - Lecture 2

CONFERENCE Recording during the thematic meeting : « Francophone Computer Algebra Days» the March 07, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIR

From playlist Mathematical Aspects of Computer Science

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Electrical Engineering: Ch 19: Fourier Transform (2 of 45) What is a Fourier Transform? Math Def

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition and equation of a Fourier transform. Next video in this series can be seen at: https://youtu.be/yl6RtWp7y4k

From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM

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Iwasawa theory of the fine Selmer groups of Galois representations by Sujatha Ramdorai

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

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An Euler System for the Symmetric Square of a Modular Form - Chris Skinner

An Euler System for the Symmetric Square of a Modular Form - Chris Skinner Joint IAS/PU Number Theory Seminar Topic: An Euler System for the Symmetric Square of a Modular Form Speaker: Chris Skinner Affiliation: Princeton University Date: February 16, 2023 I will explain a new construct

From playlist Mathematics

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To Understand the Fourier Transform, Start From Quantum Mechanics

Develop a deep understanding of the Fourier transform by appreciating the critical role it plays in quantum mechanics! Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up Sign up for my newsletter for additional physics lessons: https://www.physicswithelliot.c

From playlist Physics Mini Lessons

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Kenichi Bannai - Shintani generating class and the p-adic polylogarithm for totally real fields

The organizer is sorry for the technical problem that a part of the slides is hidden. In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke L-functions for totally real fields. In particular, we will construct

From playlist Conférences Paris Pékin Tokyo

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Fourier Transforms: Discrete Fourier Transform, Part 1

Data Science for Biologists Fourier Transforms: Discrete Fourier Transform Part 1 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

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Locally algebraic vectors in the p-adic Langlands correspondence - Gabriel Dospinescu

Gabriel Dospinescu Ecole Polytechnique March 24, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Representation Theory(Repn Th) 5 by Gerhard Hiss

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

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Fourier Transforms: Fast Fourier Transform, Part 2

Data Science for Biologists Fourier Transforms: Fast Fourier Transform Part 2 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton

From playlist Fourier

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Serre Duality on Character Varieties and Explicit Reciprocity Laws by Otmar Venjakob

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

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The discrete-time Fourier transform

The Fourier transform is arguably the most important algorithm in signal processing and communications technology (not to mention neural time series data analysis!). This video provides an in-depth, step-by-step explanation of how the Fourier transform works. The video uses files you can

From playlist OLD ANTS #2) The discrete-time Fourier transform

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Non-commutative Twisted Euler characteristic in Iwasawa theory by Sudhanshu Shekhar

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

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The Fourier Transform and Derivatives

This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow

From playlist Fourier

Related pages

Complex number | Characteristic (algebra) | Finite field | Fast Fourier transform | Normal basis | Reed–Solomon error correction | Circulant matrix | Convolution | Discrete Fourier transform