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Author : Aurel Wintner
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (89 download)
Download or read book The Fourier Transforms of Probability Distributions written by Aurel Wintner and published by . This book was released on 1947 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Fritz Oberhettinger
Publisher : Academic Press
ISBN 13 : 148321902X
Total Pages : 180 pages
Book Rating : 4.4/5 (832 download)
Download or read book Fourier Transforms of Distributions and Their Inverses written by Fritz Oberhettinger and published by Academic Press. This book was released on 2014-07-03 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.
Author : Tatsuo Kawata
Publisher : Academic Press
ISBN 13 : 148321852X
Total Pages : 681 pages
Book Rating : 4.4/5 (832 download)
Download or read book Fourier Analysis in Probability Theory written by Tatsuo Kawata and published by Academic Press. This book was released on 2014-06-17 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.
Author : Fritz Oberhettinger
Publisher : Springer Science & Business Media
ISBN 13 : 3642743498
Total Pages : 261 pages
Book Rating : 4.6/5 (427 download)
Download or read book Tables of Fourier Transforms and Fourier Transforms of Distributions written by Fritz Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of integrals of the sine-, cosine- and exponential Fourier transforms of functions f(x). It is the second, considerably enlarged version of the author's previous publication "Tabellen zur Fourier Transformation" (Springer-Verlag 1957). In addition to numerous new results in Parts I-III, a new Part IV has been introduced dealing with problems in mathematical statistics. The aim of the book is to serve as a reference work for all those whose main interest is in the application of Fourier transform methods. These methods have found a wide variety of applications in the natural and technical sciences.
Author : Robert S Strichartz
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102292
Total Pages : 236 pages
Book Rating : 4.8/5 (131 download)
Download or read book A Guide to Distribution Theory and Fourier Transforms written by Robert S Strichartz and published by World Scientific Publishing Company. This book was released on 2003-06-13 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book. A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Author : Thomas Schcker
Publisher : World Scientific
ISBN 13 : 9789810205355
Total Pages : 188 pages
Book Rating : 4.2/5 (53 download)
Download or read book Distributions, Fourier Transforms and Some of Their Applications to Physics written by Thomas Schcker and published by World Scientific. This book was released on 1991 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, distributions are introduced via sequences of functions. This approach due to Temple has two virtues: It only presupposes standard calculus.It allows to justify manipulations necessary in physical applications. The Fourier transform is defined for functions and generalized to distributions, while the Green function is defined as the outstanding application of distributions. Using Fourier transforms, the Green functions of the important linear differential equations in physics are computed. Linear algebra is reviewed with emphasis on Hilbert spaces. The author explains how linear differential operators and Fourier transforms naturally fit into this frame, a point of view that leads straight to generalized fourier transforms and systems of special functions like spherical harmonics, Hermite, Laguerre, and Bessel functions.
Author : Pierre Brémaud
Publisher : Springer
ISBN 13 : 3319095900
Total Pages : 396 pages
Book Rating : 4.3/5 (19 download)
Download or read book Fourier Analysis and Stochastic Processes written by Pierre Brémaud and published by Springer. This book was released on 2014-09-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). Each chapter has an exercise section, which makes Fourier Analysis and Stochastic Processes suitable for a graduate course in applied mathematics, as well as for self-study.
Author : I︠U︡riĭ Vladimirovich Linnik
Publisher :
ISBN 13 :
Total Pages : 266 pages
Book Rating : 4.3/5 (91 download)
Download or read book Decomposition of Probability Distributions written by I︠U︡riĭ Vladimirovich Linnik and published by . This book was released on 1964 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Academic Press
ISBN 13 : 9780080873442
Total Pages : 312 pages
Book Rating : 4.8/5 (734 download)
Download or read book Distributions and Fourier Transforms written by and published by Academic Press. This book was released on 2014-05-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributions and Fourier Transforms
Author : Saloman Bochner
Publisher : Univ of California Press
ISBN 13 : 0520345282
Total Pages : 184 pages
Book Rating : 4.5/5 (23 download)
Download or read book Harmonic Analysis and the Theory of Probability written by Saloman Bochner and published by Univ of California Press. This book was released on 2022-08-19 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Author : Walter C. Giffin
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.3/5 (91 download)
Download or read book Transform Techniques for Probability Modeling written by Walter C. Giffin and published by . This book was released on 1975 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hamish D. Meikle
Publisher : John Wiley & Sons
ISBN 13 : 3527618570
Total Pages : 238 pages
Book Rating : 4.5/5 (276 download)
Download or read book A New Twist to Fourier Transforms written by Hamish D. Meikle and published by John Wiley & Sons. This book was released on 2008-06-25 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership. The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs.
Author : J. Ian Richards
Publisher : CUP Archive
ISBN 13 : 9780521558907
Total Pages : 172 pages
Book Rating : 4.5/5 (589 download)
Download or read book The Theory of Distributions written by J. Ian Richards and published by CUP Archive. This book was released on 1995-09-29 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Author : Alexander I. Saichev
Publisher : Birkhäuser
ISBN 13 : 3319925865
Total Pages : 403 pages
Book Rating : 4.3/5 (199 download)
Download or read book Distributions in the Physical and Engineering Sciences, Volume 3 written by Alexander I. Saichev and published by Birkhäuser. This book was released on 2018-08-03 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences. Volume 1 covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and Volume 2 explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics. Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts. Distributions in the Physical and Engineering Sciences is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.
Author : Odile Pons
Publisher : World Scientific
ISBN 13 : 9811213542
Total Pages : 260 pages
Book Rating : 4.8/5 (112 download)
Download or read book Probability And Stochastic Processes: Work Examples written by Odile Pons and published by World Scientific. This book was released on 2020-03-13 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended to undergraduate students, it presents exercices and problems with rigorous solutions covering the mains subject of the course with both theory and applications.The questions are solved using simple mathematical methods: Laplace and Fourier transforms provide direct proofs of the main convergence results for sequences of random variables.The book studies a large range of distribution functions for random variables and processes: Bernoulli, multinomial, exponential, Gamma, Beta, Dirichlet, Poisson, Gaussian, Chi2, ordered variables, survival distributions and processes, Markov chains and processes, Brownian motion and bridge, diffusions, spatial processes.
Author : D. E. Newland
Publisher : Courier Corporation
ISBN 13 : 0486136965
Total Pages : 514 pages
Book Rating : 4.4/5 (861 download)
Download or read book An Introduction to Random Vibrations, Spectral & Wavelet Analysis written by D. E. Newland and published by Courier Corporation. This book was released on 2012-04-03 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of the workings of discrete wavelet transforms. Computer algorithms are explained and supported by examples and a set of problems, and an appendix lists ten computer programs for calculating and displaying wavelet transforms. Starting with an introduction to probability distributions and averages, the text examines joint probability distributions, ensemble averages, and correlation; Fourier analysis; spectral density and excitation response relations for linear systems; transmission of random vibration; statistics of narrow band processes; and accuracy of measurements. Discussions of digital spectral analysis cover discrete Fourier transforms as well as windows and smoothing. Additional topics include the fast Fourier transform; pseudo-random processes; multidimensional spectral analysis; response of continuous linear systems to stationary random excitation; and discrete wavelet analysis. Numerous diagrams and graphs clarify the text, and complicated mathematics are simplified whenever possible. This volume is suitable for upper-level undergraduates and graduate students in engineering and the applied sciences; it is also an important resource for professionals.
Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521534413
Total Pages : 468 pages
Book Rating : 4.5/5 (344 download)
Download or read book Fourier and Laplace Transforms written by and published by Cambridge University Press. This book was released on 2003-08-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 science.
