MonographDOI
Fourier and Laplace transforms
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TLDR
In this paper, the authors present in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms, which play an important role in the analysis of all kinds of physical phenomena.Abstract:
This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer scienceread more
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Journal ArticleDOI
Radial sampling for fast NMR: Concepts and practices over three decades.
TL;DR: The purpose of this article is to review the long history of radial sampling in NMR, from its initial introduction in the “accordion spectroscopy” experiments, through reduced-dimensionality and G-matrix Fourier Transform (GFT)Spectroscopy, and on to the projection spectroscopic and projection-reconstruction techniques.
Journal ArticleDOI
Event-Based Multiagent Consensus Control: Zeno-Free Triggering via $\mathcal{L}^p$ Signals
TL;DR: A Zeno-free self-triggered algorithm to achieve multiagent consensus, which enables discrete-time measurements and thus avoids continuous measurements between the neighboring agents and shows that the proposed event-based consensus algorithms guarantee less frequent triggered events in a bounded time interval.
Journal ArticleDOI
Polar Fourier transforms of radially sampled NMR data
Brian E. Coggins,Pei Zhou +1 more
TL;DR: It is shown that radially sampled data can be processed directly using Fourier transforms in polar coordinates, and an intrinsic connection between the polar Fourier transform and the filtered backprojection method that has recently been introduced to process projection-reconstruction NOESY data is described.
Journal ArticleDOI
Geometric morphometrics in entomology: Basics and applications
TL;DR: The recent expansion of a variety of morphometric tools has brought about a revolution in the comparison of morphology in the context of the size and shape in various fields including entomology.
References
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Journal ArticleDOI
Einfuhrung In Theorie Und Anwendung Der Laplace-Transformation
TL;DR: Doetsch's Handbuch der Laplace-Transformation as discussed by the authors was the first comprehensive mathematical treatise on the Laplace Transform, which was published in the early 1970s.
Book
Schaum's outline of theory and problems of Fourier analysis : with applications to boundary value problems
TL;DR: Boundary value problems Fourier series and applications Orthogonal Functions Gamma, Beta and Other Special Functions Fourier Integrals and Applications Bessel Functions and Applications Legendre Functions and applications Hermite, Laguerre and Other Orthogonals.