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Catalogue Information
Field name	Details
Dewey Class	515.2433
Title	Discrete Fourier Analysis ([Ebook]) / by M. W. Wong.
Author	Wong, M.W. (Man Wah) , 1951-
Other name(s)	SpringerLink (Online service)
Publication	Basel : Springer , 2011.
Physical Details	VIII, 177 pages, 1 illus. in color. : online resource.
Series	Pseudo-Differential Operators, Theory and Applications ; 5
ISBN	9783034801164
Summary Note	This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. Â The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Â Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.:
Contents note	Preface -- The Finite Fourier Transform -- Translation-Invariant Linear Operators -- Circulant Matrices -- Convolution Operators -- Fourier Multipliers -- Eigenvalues and Eigenfunctions -- The Fast Fourier Transform -- Time-Frequency Analysis -- Time-Frequency Localized Bases -- Wavelet Transforms and Filter Banks -- Haar Wavelets -- Daubechies Wavelets -- The Trace -- Hilbert Spaces -- Bounded Linear Operators -- Self-Adjoint Operators -- Compact Operators -- The Spectral Theorem -- Schatten-von Neumann Classes -- Fourier Series -- Fourier Multipliers on S1 -- Pseudo-Differential Operators on S1 -- Pseudo-Differential Operators on Z -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0116-4
Links to Related Works	Subject References: Abstract Harmonic Analysis . Differential equations, Partial . Fourier Analysis . Harmonic analysis . Numerical Analysis . Partial differential equations . Authors: Wong, M.W. (Man Wah) 1951- . Corporate Authors: SpringerLink (Online service) . Series: Pseudo-Differential Operators, Theory and Applications . Classification: 515.2433 . 515.2433 (DDC 23) .

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Discrete Fourier Analysis

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