TY - BOOK

T1 - Foundations of discrete harmonic analysis

AU - Malozemov, Vasily N.

AU - Masharsky, Sergey M.

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

KW - discrete harmonic analysis

KW - discrete periodic signals

KW - Discrete Fourier Transform

KW - convolution theorem

KW - correlation theorem

KW - discrete Walsh transform

KW - discrete Haar transforms

KW - discrete Ahmed-Rao bases

KW - discrete periodic splines

KW - wavelet expansions

KW - wavelet packets

KW - fast transforms

UR - http://www.scopus.com/inward/record.url?scp=85087551108&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-030-47048-7

DO - https://doi.org/10.1007/978-3-030-47048-7

M3 - Book

AN - SCOPUS:85087551108

SN - 978-3-030-47047-0

T3 - Applied and Numerical Harmonic Analysis

BT - Foundations of discrete harmonic analysis

PB - Springer Nature

CY - Switzerland

ER -