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This textbook is designed for an introductory, one-semester course in Signals and Systems for undergraduates. It is written to be concise, clear, and yet comprehensive to make it easier for the students to learn this important subject with high mathematical complexity. The popular MATLAB® software package is used for programming and simulation. Every new concept is explained with figures and examples for a clear understanding. The simple and clear style of presentation, along with comprehensive coverage, enables students to obtain a solid foundation in the subject and for use in practical applications. Written to be accessible to students of varying backgrounds, using a practical approach; Explains concepts in a clear, concise manner, minimizing mathematical rigor; Includes numerous, solved examples and exercises, as well as programming and simulations using MATLAB®.

Harmonic analysis. Fourier analysis --- Electronics --- Electrical engineering --- Computer. Automation --- Fourieranalyse --- signal processing --- elektrische circuits --- signaalprocessoren --- signaalverwerking --- Fourier transformations.

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This book provides a coherent, self-contained introduction to central topics of Analytic Partial Differential Equations in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier-Bros-Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions. The book begins by establishing the fundamental properties of analytic partial differential equations, starting with the Cauchy-Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic functionals, first in Euclidean space and, once the geometric background has been laid out, on analytic manifolds. Further topics include the proof of the Lojaciewicz inequality and the division of distributions by analytic functions, a detailed description of the Frobenius and Nagano foliations, and the Hamilton-Jacobi solutions of involutive systems of eikonal equations. The reader then enters the realm of microlocal analysis, through pseudodifferential calculus, introduced at a basic level, followed by Fourier integral operators, including those with complex phase-functions (à la Sjöstrand). This culminates in an in-depth discussion of the existence and regularity of (distribution or hyperfunction) solutions of analytic differential (and later, pseudodifferential) equations of principal type, exemplifying the usefulness of all the concepts and tools previously introduced. The final three chapters touch on the possible extension of the results to systems of over- (or under-) determined systems of these equations-a cornucopia of open problems. This book provides a unified presentation of a wealth of material that was previously restricted to research articles. In contrast to existing monographs, the approach of the book is analytic rather than algebraic, and tools such as sheaf cohomology, stratification theory of analytic varieties and symplectic geometry are used sparingly and introduced as required. The first half of the book is mainly pedagogical in intent, accessible to advanced graduate students and postdocs, while the second, more specialized part is intended as a reference for researchers.

Algebraic geometry --- Differential geometry. Global analysis --- Harmonic analysis. Fourier analysis --- Differential equations --- Mathematics --- Fourieranalyse --- differentiaalvergelijkingen --- topologie (wiskunde) --- statistiek --- wiskunde --- geometrie --- Differential equations, Partial. --- Equacions en derivades parcials

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Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explaine

Harmonic analysis. Fourier analysis --- Mathematical control systems --- Electronics --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- geluidsleer --- digitale signaalverwerking --- beeldverwerking --- Fourieranalyse --- signaalverwerking --- Statistical methods --- Mathematical models --- Data processing --- signals --- Signal processing --- Wavelets (Mathematics) --- Mathematics. --- Mathematics --- 534 --- 534 Vibrations. Acoustics --- Vibrations. Acoustics --- Wavelet analysis --- Harmonic analysis --- Signal processing - Mathematics

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mathematics --- Fourieranalyse --- analyse (wiskunde) --- Harmonic analysis. Fourier analysis --- wiskunde --- Boundary value problems --- Fourier analysis --- differentiaal --- fourieranalyse --- integraal --- 517 --- Analyse : Besselfuncties --- Analyse : Fourier analyse --- Analyse : Fourier transformaties --- Veelterminterpolatie --- #TWER:MOD --- 517.44 --- 517.44 Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Analysis, Fourier --- Mathematical analysis --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Analyse de Fourier --- Problèmes aux limites --- Fourier, Analyse de --- Boundary value problems. --- Fourier analysis. --- Basic Sciences. Mathematics --- Applied Mathematics. --- Fourier Analysis --- Fourier, Séries de --- Trigonométrie --- Exercices corriges --- Schaum --- Mathematiques superieures --- Analyse mathematique --- Serie de fourier --- Fonction periodique --- Fonction gamma --- Fonction de bessel --- Fonction de legendre --- Transformee de fourier

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Numerical analysis --- -681.3*G1 --- #WBIB:dd.Lic.L.De Busschere --- Analyse (wiskunde) --- Extrapolatie --- Intrapolatie --- Numerieke analyse --- 167 --- 519.6 --- numerieke analyse --- 681.3*G1 Numerical analysis --- Mathematical analysis --- Problems, exercises, etc --- 681.3*G1 --- 51(076.1) --- differentiaalvergelijkingen --- differentialen --- eigenvalues --- eigenvectoren --- eindige verschillen --- extrapolatie --- fortran --- fourieranalyse --- foutenanalyse --- integralen --- interpolatie --- kleinste kwadraten --- lineaire algebra --- lineaire programmering --- matrices --- Monte Carlo --- niet-lineaire vergelijkingen --- oefeningen --- operationeel onderzoek --- partiële differentiaalvergelijkingen --- reeksen --- software --- wiskunde --- computerwiskunde --- probleemoplossend denken --- algoritmen --- Problems, exercises, etc. --- Analyse numérique.