Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing

Roe W Goodman (,

ISBN 10: 9814725765 ISBN 13: 9789814725767

Published by World Scientific Publishing Company, 2016

Language: English

Condition: New Hardcover

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Bibliographic Details

Title

Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing

Publisher

World Scientific Publishing Company

Publication Date

2016

Language

English

ISBN 10

9814725765

ISBN 13

9789814725767

Binding

Hardcover

Condition

Brand New

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Synopsis

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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