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Single-shot extended-depth-of-field fourier light field microscopy enabled by a distorted grating. [PDF]

Biomed Opt Express
Huang J, Zhang X, Deng Z, Zhang J, Li H, Ni Y, Chen D, Qu J.   +7 more
europepmc   +1 more source

Bandgap characteristics and optimization of two-dimensional phononic metamaterials with functionally graded rings. [PDF]

Sci Rep
Li Q, Wang J.
europepmc   +1 more source

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Fourier-Haar coefficients

Mathematical Notes of the Academy of Sciences of the USSR, 1984
A Banach lattice E is called p-concave, \(1\leq ...
Novikov, I. Ya., Semenov, E. M.
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ON FOURIER COEFFICIENTS

Mathematics of the USSR-Sbornik, 1981
Let be an orthonormal system of functions on the interval , and let the function . We investigate the question of the convergence or divergence (depending on the smoothness of the function ) of series of the form where or with .It is shown that in a certain sense, the assertions obtained are definitive for the Haar system.Bibliography: 14 titles.
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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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Estimates of Fourier Coefficients

gmj, 2003
Abstract Some well-known properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems.
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On the magnitude of Vilenkin–Fourier coefficients

European Journal of Mathematics, 2020
Let us denote \(P=\{p_n\}\) a sequence of natural numbers, such that, \(p_n\geq 2\), \(\forall n\in\mathbb{N}\) and Let \(m_0=1\), \(m_n=p_nm_{n-1}\). Then, every \(x\in[0,1)\) can be written as \(x=\sum_{n=1}^{\infty}\frac{x_n}{m_n}\), where \(x_n\in\mathbb{Z}\cap[0,p_n)\).
Volosivets, Sergey S., Kuznetsova, Maria A.   +1 more
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The Möbius inversion and Fourier coefficients

Applied Mathematics and Computation, 2001
The authors show that an analogue of the Möbius inversion formula in a commutative semigroup with unique factorization can be used to study \(n\)-dimensional Fourier coefficients. The authors utilize to this aim an arbitrary algebraic number field of degree \(n\), whose ring of integers is a unique factorization domain.
Zhao-Dou Chen, Yanan Shen, Jun Ding
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On the Order of Magnitude of Fourier Coefficients

SIAM Journal on Mathematical Analysis, 1986
Let f(t) be of period 2, f(t)\(\in L(-1,1)\). Let its Fourier cosine and sine coefficients be respectively \(a_ m,b_ n\). It is familiar that \(a_ n\to 0\), \(b_ n\to 0\) as \(n\to \infty\). Even if we restrict ourselves to the case in which f(t) is continuous, these results are best possible in the sense that, given any sequence \(\{k_ n\}\) with ...
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