Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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Book•
01 Jan 1950
TL;DR: Carlaw's theory of Fourier's series and integrals as mentioned in this paper is a well-known work on the theory of series and integral analysis, and it is of this work that the present book is the new edition.
Abstract: PROF. CARSLAW'S excellent book is so well known that it needs little general introduction. The first edition, published in 1906, was a work on “Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat”. The second edition followed in 1921, in two volumes. The great advances in the theory of Fourier's series had caused the earlier chapters to develop into a self-contained book on analysis, including much matter on sequences and integration in addition to the theory of Fourier's series. It is of this work that the present book is the new edition.Introduction to the Theory of Fourier's Series and Integrals.Prof. H. S. Carslaw. Third edition, revised and enlarged. Pp. xiii + 368. (London: Macmillan and Co., Ltd., 1930.) 20s. net.
254 citations
253 citations
TL;DR: Based on the (m, N, q)-regular Fourier matrix, a new algorithm is proposed for fast Fourier transform (FFT) of nonuniform (unequally spaced) data with accuracy much better than previously reported results with the same computation complexity.
Abstract: Based on the (m, N, q)-regular Fourier matrix, a new algorithm is proposed for fast Fourier transform (FFT) of nonuniform (unequally spaced) data. Numerical results show that the accuracy of this algorithm is much better than previously reported results with the same computation complexity of O(N log/sub 2/ N). Numerical examples are shown for the applications in computational electromagnetics.
251 citations
Book•
17 Jul 2003
TL;DR: In this article, the ubiquitous convolution was used for multidimensional Fourier analysis and the Discrete Fourier Transform (DFT) transform was used to transform the Fourier series into a discrete Fourier transform.
Abstract: Introduction.- Preparations.- Laplace and Z Transforms.- Fourier Series.- L^2 Theory.- Separation of Variables.- Fourier Transforms.- Distributions.- Multi-Dimensional Fourier Analysis.- Appendix A: The ubiquitous convolution.- Appendix B: The Discrete Fourier Transform.- Appendix C: Formulae.- Appendix D: Answers to exercises.- Appendix E: Literature.
248 citations