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Start Over Subject Fourier transform

1. A note on the convolution theorem for the Fourier transform

Creator:
Kahane, Charles S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convolution and Fourier transform
Language:
English
Description:
In this paper we characterize those bounded linear transformations $Tf$ carrying $L^{1}( \mathbb {R}^{1}) $ into the space of bounded continuous functions on $\mathbb {R}^{1}$, for which the convolution identity $T(f\ast g) =Tf\cdot Tg $ holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Asymptotics of variance of the lattice point count

Creator:
Janáček, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
point lattice, Fourier transform, volume, and variance
Language:
English
Description:
The variance of the number of lattice points inside the dilated bounded set $rD$ with random position in $\Bbb R^d$ has asymptotics $\sim r^{d-1}$ if the rotational average of the squared modulus of the Fourier transform of the set is $O(\rho ^{-d-1})$. The asymptotics follow from Wiener's Tauberian theorem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Detection of vigilance changes by linear and nonlinear EEG signal analysis

Creator:
Svoboda, Petr
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Fourier transform, linear analysis, nonlinear analysis, state-space trajectory, attractor, embedding dimension, delay time embedding, fractal dimension, electroencephalography, microsleep, and Human Machine Interface (HMI)
Language:
English
Description:
This paper presents advanced methodology for the analysis of the electroencephalographic activity (EEG) of the brain aimed to monitor the cognitive states of an operator. The methodology of EEG analysis is based on two main approaches: linear methods based on Fourier transform, Linear Stochastic Models, Multi-covariance analysis, and nonlinear methods based on estimation of state space attractor, state space dimension, D2 dimension and the Largest Lyapunov Exponent (LLE). The correct application of these methods is supported by the study of stability, dynamics and space distribution of EEG signal. The uncertainty of adopting a new methodology, such as presented chaos theory, for EEG signal analysis is minimized by the adequate setup of experiments and by evaluation of results against well adopted power spectral estimates calculated by Fourier transform. For better understanding of the underlying processes behind EEG, the basic mental states such as relaxation, single and complex number count, and Raven test are analyzed and compared with the vigilance states. The averaged behavior of the computed markers of the EEG signal is studied with respect to a reaction time scale by the evaluation of a set of experiments. Because of this complex approach, the presented methodology is able to track the ongoing changes in EEG activity during the process of falling asleep. The automatic detection of vigilance changes is a consequent step to this work. Usability of such device in various fields of everyday life is of the high importance.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Generalized Hermitean ultradistributions

Creator:
Andrade, C. and Loura, L.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
distribution, multipole series, Fourier transform, complex translation, and ultradistribution
Language:
English
Description:
In this paper we define, by duality methods, a space of ultradistributions G ′ ω(RN ). This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two. The method used to construct G ′ ω(RN ) led us to a detailed study, presented at the beginning of the paper, of the duals of infinite dimensional locally convex spaces that are inductive limits of finite dimensional subspaces.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Some results about the Henstock-Kurzweil Fourier transform

Creator:
Mendoza Torres, Francisco J., Escamilla Reyna, Juan A., and Sánchez Perales, Salvador
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Fourier transform, Henstock-Kurzweil integral, and bounded variation functions
Language:
English
Description:
We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public