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The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.

Hilbert transform --- Hilbert transform. --- Polynomen. --- Vergelijkingen (wiskunde) --- Vergelijkingen (wiskunde). --- Transform, Hilbert --- Integral transforms --- Hilbert, transformation de

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Signal processing --- Hilbert transform. --- Software radio --- Digital techniques.

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Transformations (Mathematics) --- Algorithms --- Differential invariants --- Geometry, Differential --- Fourier transform, Hilbert transform, Riesz trransform.

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The Hilbert-Huang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the Wigner-Ville Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics - the artif

Hilbert-Huang transform. --- Decomposition (Mathematics) --- Mathematics --- Probabilities --- EMD-HSA method --- Empirical mode decomposition method --- HHT (Hilbert-Huang transform) --- Hilbert transform --- Time-series analysis

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Analytical spaces --- Harmonic analysis. Fourier analysis --- Algebraic topology --- Harmonic analysis. --- Hilbert transform. --- Vector fields. --- Analyse harmonique --- Transformation de Hilbert --- Champs vectoriels --- Stein, Elias M., --- 51 <082.1> --- Mathematics--Series --- Harmonic analysis --- Hilbert transform --- Vector fields --- Direction fields (Mathematics) --- Fields, Direction (Mathematics) --- Fields, Slope (Mathematics) --- Fields, Vector --- Slope fields (Mathematics) --- Vector analysis --- Transform, Hilbert --- Integral transforms --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Stein, E. M. --- Steĭn, Ilaĭes M., --- Стейн, Илайес М.,