Authors:
- Provides a self-contained introduction to discrete harmonic analysis
- Builds an advanced theory from scratch that can be applied to signal processing
- Includes about 150 exercises, with solutions
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
Part of the book sub series: Lecture Notes in Applied and Numerical Harmonic Analysis (LN-ANHA)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (4 chapters)
-
Front Matter
-
Back Matter
About this book
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 processing.
Authors and Affiliations
-
Mathematics and Mechanics Faculty, Saint Petersburg State University, Saint Petersburg, Russia
Vasily N. Malozemov, Sergey M. Masharsky
About the authors
Vasily N. Malozemov, Doctor of Science, is professor at the Mathematics and Mechanics Faculty of Saint Petersburg University. His main scientific interests lie in the field of discrete harmonic analysis, spline theory, Chebyshev approximations and nonsmooth optimization, and fast algorithms.
Sergey M. Masharsky, Ph. D., is associate professor at the Mathematics and Mechanics Faculty of Saint Petersburg University. His main scientific interests lie in the field of discrete harmonic analysis and fast algorithms.
Bibliographic Information
Book Title: Foundations of Discrete Harmonic Analysis
Authors: Vasily N. Malozemov, Sergey M. Masharsky
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-030-47048-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-47047-0Published: 24 June 2020
eBook ISBN: 978-3-030-47048-7Published: 24 June 2020
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XV, 247
Number of Illustrations: 20 b/w illustrations, 1 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Signal, Image and Speech Processing, Fourier Analysis