Browsing by Subject "Impulse functions"

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    A class of impulsive eigenfunctions of multidimensional Fourier transform
    (IEEE, 2024-03-04) Onural, Levent
    The coordinate axes of ${\mathbb {R}}^{N}$ are arbitrarily partitioned into two sets; each set defines a hyperplane passing through the origin and these two hyperplanes are orthogonal. After a review of impulse functions over such hyperplanes and their Fourier transforms, it is shown that an impulse function over the union of these two hyperplanes is an eigenfunction of the $N$-dimensional Fourier transform. Furthermore, based on the simple rotation property of the Fourier transform, it is also shown that impulse functions over unions of finite number of arbitrarily rotated versions of those two hyperplane sets are also eigenfunctions of the $N$-dimensional Fourier transform.
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    ItemOpen Access
    Impulse functions over curves and surfaces and their applications to diffraction
    (Elsevier Science & Technology, 2006-10-01) Onural, L.
    An explicit preferred definition of impulse functions (Dirac delta functions) over lowerdimensional manifolds in RN is given in such a way to assure uniform concentration per geometric unit of the manifold. Some related properties are presented. An application related to diffraction is demonstrated.
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    ItemOpen Access
    Projection-slice theorem as a tool for mathematical representation of diffraction
    (Institute of Electrical and Electronics Engineers, 2007) Onural, L.
    Although the impulse (Dirac delta) function has been widely used as a tool in signal processing, its more complicated counterpart, the impulse function over higher dimensional manifolds in ℝN, did not get such a widespread utilization. Based on carefully made definitions of such functions, it is shown that many higher dimensional signal processing problems can be better formulated, yielding more insight and flexibility, using these tools. The well-known projection-slice theorem is revisited using these impulse functions. As a demonstration of the utility of the projection-slice formulation using impulse functions over hyperplanes, the scalar optical diffraction is reformulated in a more general context.