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

By: Publication details: World scientific 2016 SingaporeDescription: xii, 288 pISBN:
  • 9789814725774
Subject(s): DDC classification:
  • 515.723 G6D4
Summary: 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. http://www.worldscientific.com/worldscibooks/10.1142/9835
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Books Vikram Sarabhai Library Rack 28-A / Slot 1380 (0 Floor, East Wing) Non-fiction General Stacks 515.723 G6D4 (Browse shelf(Opens below)) Available 194911

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.



http://www.worldscientific.com/worldscibooks/10.1142/9835

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