Title Details: | |
Fourier transform |
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Authors: |
Tsitsas, Nikolaos |
Reviewer: |
Frantzeskakis, Dimitrios |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE > SERIES EXPANSIONS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS > GENERAL THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PARTIAL DIFFERENTIAL EQUATIONS > GENERAL HIGHER-ORDER EQUATIONS AND SYSTEMS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS |
Description: | |
Abstract: |
The continuous Fourier transform is a generalization of the Fourier series. It offers representations of functions, which are defined on infinite intervals and are not necessarily periodic, as superpositions of sinusoidal functions. It is a useful mathematical tool for studying numerous applications in areas such as communications, signal processing, and wave phenomena. Like the Laplace transform and the Fourier transform it is a member of a class of representations known as integral transforms. In this sense it is used in solving differential equations. Moreover, in Information Theory it allows the examination of a waveform in both the time and frequency domains. In this chapter the concept of the Fourier transform is defined and its basic properties are formulated. Characteristic Fourier transforms of important functions are calculated and some basic applications are formulated and worked out.
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Type: |
Chapter |
Creation Date: | 2015 |
Item Details: | |
License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
Handle | http://hdl.handle.net/11419/1143 |
Bibliographic Reference: | Tsitsas, N. (2015). Fourier transform [Chapter]. In Tsitsas, N. 2015. Applied Mathematics [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1143 |
Language: |
Greek |
Is Part of: |
Applied Mathematics |
Publication Origin: |
Kallipos, Open Academic Editions |