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During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Stochastic processes --- Analytical topology --- Frames (Vector analysis) --- Bases (Linear topological spaces) --- Signal processing --- Cadres (Analyse vectorielle) --- Bases (Espaces vectoriels topologiques) --- Traitement du signal --- Mathematics. --- Mathématiques --- Mathematics --- Bases (Linear topological spaces). --- Frames (Vector analysis). --- Signal processing -- Mathematics. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Basis theory (Linear topological spaces) --- Frame theory (Vector analysis) --- Harmonic analysis. --- Fourier analysis. --- Functional analysis. --- Operator theory. --- Mathematical models. --- Functional Analysis. --- Fourier Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Signal, Image and Speech Processing. --- Abstract Harmonic Analysis. --- Operator Theory. --- Linear topological spaces --- Sequences (Mathematics) --- Vector analysis --- Functional analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analysis, Fourier --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Models, Mathematical --- Simulation methods --- Signal processing - Mathematics