Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach
The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as betw...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2015-12-01
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| Series: | Cogent Education |
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| Online Access: | http://dx.doi.org/10.1080/2331186X.2015.1064560 |
| _version_ | 1797711561841704960 |
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| author | Ludwig Kohaupt |
| author_facet | Ludwig Kohaupt |
| author_sort | Ludwig Kohaupt |
| collection | DOAJ |
| description | The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT) plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT); this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time) Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations. |
| first_indexed | 2024-03-12T07:07:47Z |
| format | Article |
| id | doaj.art-1172a8b3296f43a9b14f9262910d3a18 |
| institution | Directory Open Access Journal |
| issn | 2331-186X |
| language | English |
| last_indexed | 2024-03-12T07:07:47Z |
| publishDate | 2015-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Cogent Education |
| spelling | doaj.art-1172a8b3296f43a9b14f9262910d3a182023-09-02T23:16:33ZengTaylor & Francis GroupCogent Education2331-186X2015-12-012110.1080/2331186X.2015.10645601064560Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approachLudwig Kohaupt0Beuth University of Technology BerlinThe discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT) plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT); this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time) Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations.http://dx.doi.org/10.1080/2331186X.2015.1064560discrete Fourier seriesmathematical and engineering aspectsdiscrete Fourier transform (DFT)fast Fourier transform (FFT) |
| spellingShingle | Ludwig Kohaupt Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach Cogent Education discrete Fourier series mathematical and engineering aspects discrete Fourier transform (DFT) fast Fourier transform (FFT) |
| title | Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach |
| title_full | Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach |
| title_fullStr | Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach |
| title_full_unstemmed | Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach |
| title_short | Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach |
| title_sort | introduction to the discrete fourier series considering both mathematical and engineering aspects a linear algebra approach |
| topic | discrete Fourier series mathematical and engineering aspects discrete Fourier transform (DFT) fast Fourier transform (FFT) |
| url | http://dx.doi.org/10.1080/2331186X.2015.1064560 |
| work_keys_str_mv | AT ludwigkohaupt introductiontothediscretefourierseriesconsideringbothmathematicalandengineeringaspectsalinearalgebraapproach |