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Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Four...

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Detalles Bibliográficos
Autor principal: Goodman, Roe W
Lenguaje:eng
Publicado: World Scientific 2016
Materias:
Acceso en línea:http://cds.cern.ch/record/2220355
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author Goodman, Roe W
author_facet Goodman, Roe W
author_sort Goodman, Roe W
collection CERN
description This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-22203552021-04-21T19:30:40Zhttp://cds.cern.ch/record/2220355engGoodman, Roe WDiscrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processingMathematical Physics and MathematicsThis textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.World Scientificoai:cds.cern.ch:22203552016
spellingShingle Mathematical Physics and Mathematics
Goodman, Roe W
Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
title Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
title_full Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
title_fullStr Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
title_full_unstemmed Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
title_short Discrete Fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
title_sort discrete fourier and wavelet transforms: an introduction through linear algebra with applications to signal processing
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2220355
work_keys_str_mv AT goodmanroew discretefourierandwavelettransformsanintroductionthroughlinearalgebrawithapplicationstosignalprocessing