Lecture

Fourier Transform: Inversion Formula

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In course

MATH-203(b): Analysis III

Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour résoudre des problèmes pluridisciplinaires d'ingénierie scientifique. ...

Description

This lecture covers the Fourier Transform inversion formula, exploring examples and applications. It delves into the concept of transforming functions and the process of finding the inverse of a function using Fourier Transform. The instructor demonstrates how to apply the inversion formula in various scenarios, emphasizing the importance of understanding the Fourier Transform for signal processing and analysis.

Instructors (2)

David Valentin Strütt

Assistanat Vous visitez cette page dans l'optique de rejoindre mon équipe d'asssistant·es pour un de mes cours d'analyse ? Vous trouverez plus d'informations ici. Contributions auteur de polycopiés d'analysecréateur matheminecraftrecord suisse du plus grand nombre de participations à la construction d'un additionneur binaire en dominos (autoproclamé) Je suis né pile le jour de mon anniversaire. Expériences professionnelles Chargé de communication pour MATH et chargé de cours pour la SMA 2019–2024 EPFLCharg

Maria Colombo

Teaching & PhD PhD Students Roberto Colombo, Antonio Tirotta, Carl Johan Peter Johansson, Giulia Mescolini Past EPFL PhD Students Luigi De Rosa, Silja Noëmi Aline Haffter, Massimo Sorella Courses Analysis IV - Lebesgue measure, Fourier analysis MATH-205 Learn the basis of Lebesgue integration and Fourier analysis Topics on the Euler and Navier-Stokes equations MATH-647 This topics course focuses on recent and classical fundamental results on the Euler and Navier-Stokes equa

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Related concepts (32)

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Signal processing

Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, , potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. According to Alan V. Oppenheim and Ronald W.

Digital signal processing

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.

Discrete-time Fourier transform

In mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.

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