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Foundations of Discrete Harmonic Analysis

Foundations of Discrete Harmonic Analysis

Wydawnictwo Springer Nature Switzerland AG
Data wydania 24/06/2020
Liczba stron 247
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9783030470470
Kategorie Analizy funkcjonalne i przekształcenia, Analiza numeryczna, Systemy i technologie powstawiania obrazów
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Opis książki

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.

Foundations of Discrete Harmonic Analysis

Spis treści

1 Preliminaries.- 2 Signal Transforms.- 3 Spline Subspaces.- 4 Fast Algorithms.- Solutions.- References.- Index.

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