Results 241 to 250 of about 471,906 (281)

On Density of Fourier Coefficients

Canadian Mathematical Bulletin, 1973
Letfbe anLintegrable real valued function of period 2π and let(1)be its Fourier series. It is known that iffis of bounded variation then allnanandnbn(n=1,2,3,…) lie in the interval [-V(F)/π, V(F)/π;] whereV(f) is the total variation off. M. Izumi and S.
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The calculation of Fourier Coefficients

SIAM Journal on Numerical Analysis, 1967
where q is a positive integer and f(x) is a real function which, together with its first 2p derivatives, is continuous in the interval [0, 1]. The method involves calculating trapezoidal rule approximationsto 1 f(t) dt with different mesh ratios and combining these results. In the case that f(x) is a periodic function with period 1, this method reduces
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Estimation of Fourier coefficients

IEEE Transactions on Instrumentation and Measurement, 1989
It is shown that the maximum-likelihood estimation or robust estimation of the Fourier coefficients may be preferable to Fourier transformation if the noise contains outliers or is otherwise not normally distributed. The reason is that, in that case, these estimators produce Fourier coefficient estimates and, therefore, system parameter estimates ...
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Fourier coefficient harmonic analyzer

Electrical Engineering, 1949
THE SEPARATION of a complex curve into its constituent sine and cosine curves of proper amplitude and phase by means of a Fourier series analysis is well known, and this method is frequently used in many branches of engineering and mathematics. All who have ever made such an analysis know that the computation for the Fourier coefficients can be very ...
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FOURIER EXPANSIONS WITH MODULAR FORM COEFFICIENTS

International Journal of Number Theory, 2009
In this paper, we study the Fourier expansion where the coefficients are given as the evaluation of a sequence of modular forms at a fixed point in the upper half-plane. We show that for prime levels l for which the modular curve X0(l) is hyperelliptic (with hyperelliptic involution of the Atkin–Lehner type) then one can choose a sequence of weight k (
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Uniform approximation by Fourier–Stieltjes coefficients

Mathematical Proceedings of the Cambridge Philosophical Society, 1968
In chapter I, E = {nk} ⊂ Z is shown to be a Sidon set if and only if (**). For each x ∈ T,.Let E ⊂ Z+ be a lacunary sequence. In chapter II, it is constructively shown that the characteristic function of E is uniformly approximable by Fourier–Stieltjes coefficients; i.e. ϕE ∈ M(T)∧−.
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Generalized Lipschitz Classes and Fourier Coefficients

Mathematical Notes, 2004
The author proves several general results. Among others he gives a criterion for a function to belong to the generalized Lipschitz class defined by using moduli of smoothness of positive orders and presents necessary and sufficient conditions for this criterion to hold.
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On a Sequence of Fourier Coefficients

Proceedings of the American Mathematical Society, 1959
This method of summability, known as harmonic summability, was introduced by Riesz in 1924 [5]. This method is regular [5]. We obtain another method of summation viz., (N, 1/(n+1)). Ci by superimposing the method (N, 1/(n+1)) on the Cesaro means of order one. 1.2. Let f(t) be a function which is integrable in the sense of Lebesgue over the interval (ir,
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Concept, implementations and applications of Fourier ptychography

Nature Reviews Physics, 2021
Guoan Zheng, Cheng Shen, Shaowei Jiang
exaly  

Phases of Fourier Coefficients

2016
We have explored in great depth one dimension of Fourier coefficients, their magnitude. This has proved a worthwhile journey, with incontrovertible musical meaning; it allows the painting of nice pictures of scales/chords landscapes, though with the major and embarrassing restriction that scales must share their cardinality in pictures such as Fig. 5.3;
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