3,547 research outputs found
Two new convolutions for the fractional Fourier transform
In this paper we introduce two novel convolutions for the fractional Fourier transforms (FRFT), and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish a necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in L^1(R) and L^2(R) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper
Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems
Convolution products for hypercomplex Fourier transforms
Hypercomplex Fourier transforms are increasingly used in signal processing
for the analysis of higher-dimensional signals such as color images. A main
stumbling block for further applications, in particular concerning filter
design in the Fourier domain, is the lack of a proper convolution theorem. The
present paper develops and studies two conceptually new ways to define
convolution products for such transforms. As a by-product, convolution theorems
are obtained that will enable the development and fast implementation of new
filters for quaternionic signals and systems, as well as for their higher
dimensional counterparts.Comment: 18 pages, two columns, accepted in J. Math. Imaging Visio
Five Years of Continuous-time Random Walks in Econophysics
This paper is a short review on the application of continuos-time random
walks to Econophysics in the last five years.Comment: 14 pages. Paper presented at WEHIA 2004, Kyoto, Japa
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: Sampling Cost via Incident-Field Windowing and Recentering
This paper proposes a frequency/time hybrid integral-equation method for the
time dependent wave equation in two and three-dimensional spatial domains.
Relying on Fourier Transformation in time, the method utilizes a fixed
(time-independent) number of frequency-domain integral-equation solutions to
evaluate, with superalgebraically-small errors, time domain solutions for
arbitrarily long times. The approach relies on two main elements, namely, 1) A
smooth time-windowing methodology that enables accurate band-limited
representations for arbitrarily-long time signals, and 2) A novel Fourier
transform approach which, in a time-parallel manner and without causing
spurious periodicity effects, delivers numerically dispersionless
spectrally-accurate solutions. A similar hybrid technique can be obtained on
the basis of Laplace transforms instead of Fourier transforms, but we do not
consider the Laplace-based method in the present contribution. The algorithm
can handle dispersive media, it can tackle complex physical structures, it
enables parallelization in time in a straightforward manner, and it allows for
time leaping---that is, solution sampling at any given time at
-bounded sampling cost, for arbitrarily large values of ,
and without requirement of evaluation of the solution at intermediate times.
The proposed frequency-time hybridization strategy, which generalizes to any
linear partial differential equation in the time domain for which
frequency-domain solutions can be obtained (including e.g. the time-domain
Maxwell equations), and which is applicable in a wide range of scientific and
engineering contexts, provides significant advantages over other available
alternatives such as volumetric discretization, time-domain integral equations,
and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now
including direct comparisons to existing CQ and TDIE solver implementations)
(Part I of II
Laplace-Laplace analysis of the fractional Poisson process
We generate the fractional Poisson process by subordinating the standard
Poisson process to the inverse stable subordinator. Our analysis is based on
application of the Laplace transform with respect to both arguments of the
evolving probability densities.Comment: 20 pages. Some text may overlap with our E-prints: arXiv:1305.3074,
arXiv:1210.8414, arXiv:1104.404
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