Foundations of discrete harmonic analysis
By: Malozemov, Vasily N.
Contributor(s): Masharsky, Sergey M.
Series: Lecture notes in applied and numerical haromonic analysis. / edited by John J. Benedetto.Publisher: Switzerland Birkhauser 2020Description: xv, 247p.ISBN: 9783030470470.Subject(s): Harmonic analysis | Numerical analysis | Functional analysis and transformsDDC classification: 5152433 | M298f Summary: This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing. In a nutshell, DHA is used to determine the time-frequency structure of a digitized signal, providing a representation of the signal as a sum of spectral components that can then be analyzed.The main methods of DHA are discrete Fourier transform and other discrete orthogonal transforms such as the Walsh and Haar transforms. Fast algorithms are used to process signals in real time, while additional options are provided by spline harmonic analysis. These topics are carefully covered in the book. With only modest prerequisites, some of which are recalled at the beginning, a profound mathematical theory is built almost from scratch. The 150 exercises included form an integral part of the text.Based decades of teaching experience, this book provides a basis for lecture courses starting at the upper undergraduate level, and will also prove a valuable resource for mathematicians and engineers interested in digital signal| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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PK Kelkar Library, IIT Kanpur | On Display | 5152433 M298f (Browse shelf) | Available | A186657 |
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This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing. In a nutshell, DHA is used to determine the time-frequency structure of a digitized signal, providing a representation of the signal as a sum of spectral components that can then be analyzed.The main methods of DHA are discrete Fourier transform and other discrete orthogonal transforms such as the Walsh and Haar transforms. Fast algorithms are used to process signals in real time, while additional options are provided by spline harmonic analysis. These topics are carefully covered in the book. With only modest prerequisites, some of which are recalled at the beginning, a profound mathematical theory is built almost from scratch. The 150 exercises included form an integral part of the text.Based decades of teaching experience, this book provides a basis for lecture courses starting at the upper undergraduate level, and will also prove a valuable resource for mathematicians and engineers interested in digital signal
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