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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TL;DR: For the complete system of the orthogonal Walsh functions, the implementation of circuits by modem semiconductor techniques appears to be competitive in a number of applications with the implementationof circuits for the system of sine and cosine functions.
Abstract: The system of sine and cosine functions has been distinguished historically in communications. Whenever the term frequency is used, reference is made implicitly to these functions; hence the generally used theory of communication is based on the system of sine and cosine functions. In recent years other complete systems of orthogonal functions have been used for theoretical investigations as well as for equipment design. Analogs to Fourier series, Fourier transform, frequency, power spectra, and amplitude, phase, and frequency modulation exist for many systems of orthogonal functions. This implies that theories of communication can be worked out on the basis of these systems. Most of these theories are of academic interest only. However, for the complete system of the orthogonal Walsh functions, the implementation of circuits by modem semiconductor techniques appears to be competitive in a number of applications with the implementation of circuits for the system of sine and cosine functions.
81 citations
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TL;DR: In this paper, a usable characterization of the group Fourier transform of Schwartz space on the Heisenberg group H n, in terms of certain asymptotic series was derived.
81 citations
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TL;DR: A method for generating near optimal trajectories of linear and nonlinear dynamic systems, represented by deterministic, lumped-parameter models, is proposed based on a Fourier series approximation of each generalized coordinate that converts the optimal control problem into an algebraic nonlinear programming problem.
Abstract: A method for generating near optimal trajectories of linear and nonlinear dynamic systems, represented by deterministic, lumped-parameter models, is proposed. The method is based on a Fourier series approximation of each generalized coordinate that converts the optimal control problem into an algebraic nonlinear programming problem. The results of computer simulation studies compare favorably to optimal solutions obtained by closed-form analyses and/or by other numerical schemes
81 citations
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TL;DR: In this article, it was shown that if the series converges at every point of an interval (a, b) to a finite and integrable function f(x), then the series behaves essentially like a Fourier series.
Abstract: whose coefficients are expressed by the very well known formulas. The tests we have at our disposal for the convergence or summability of Fourier series are perfectly satisfactory for applications of Fourier series. In a number of problems we come across series which are of the form (1.1.1) without necessarily being Fourier series. Such series are the object of Riemann's theory of trigonometric series. This theory shows e.g. that if the series converges at every point of an interval (a, b) to a finite and integrable function f(x), then the series behaves essentially like a Fourier series. More precisely, if f*(x) is any integrable function of period 27r coinciding with f(x) in (a, b), and if
81 citations
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TL;DR: In this paper, a new class of amplitude transformers was designed using the design method described by Eisner and Seager, in which a suitable wave function is chosen and the corresponding profile is deduced, and the wave function used is a fourth-order Fourier series.
Abstract: Using the design method described by Eisner and Seager, in which a suitable wavefunction is chosen and the corresponding profile is deduced, a new class of amplitude transformers is designed. The wavefunction used is a fourth‐order Fourier series. The resulting transformers give a useful compromise between the properties of the “stepped” and the “exponential” transformers. The output amplitude produced for a given maximum strain is somewhat lower than the amplitude given by the exponential transformer of the same magnification, but is much higher than that given by the corresponding stepped transformer. While the “Fourier” transformer is slightly less stiff in bending than the stepped, it is very much stiffer than the exponential.
81 citations