DISCRETE MELLIN CONVOLUTION WITH DILATION AND ITS APPLICATIONS

Discrete Fresnel Transform and Its Circular Convolution

 Abstract—Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for Fourier transform. In this letter, we derive a discrete Fresnel transform (DFnT) from the infinitely periodic optical gratings, as a linear trigon...

Generalized Product Theorem for the Mellin Transform and Its Applications

the past hospitalization and its association with suicide attempts and ideation in patients with mdd and comparison with bmd (depressed type) group

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Mellin Convolution for Signal Filtering and Its Application to the Gaussianization of Lévy Noise

Noises are usually assumed to be Gaussian so that many existing signal processing techniques can be applied with no worry. However, in many real world natural or man-made systems, noises are usually heavy-tailed. It is increasingly desirable to address the problem of finding an opportune filter function for a given input noise in order to generate a desired output noise. By filtering theory, th...

Discrete spacetime and its applications

A discrete spacetime is a random partially ordered set. It is obtained by sampling n points from a compact domain in a spacetime manifold w.r.t. the volume form. The partial order is given by restricting the causal structure on the domain to the sampled points. These objects were introduced by physicists in an attempt to reconcile gravity with quantum mechanics, [39, 45, 18]. They received very...