Recently, a 'gammachirp' function has been derived as an optimal auditory filter function in terms of minimal uncertainty in a joint time and modified-scale representation if the scale transform defined by Cohen is used in the auditory system. The gammatone function, which is widely used as the impulse response of a linear auditory filter, is a first-order approximation of the 'gammachirp' func...

In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

This paper presents a novel method for classifying an image into one of predeened classes in a data bank by applying mutual information to a representation of the Fourier amplitude domain. Template and test images are made translation and rotation invariant through the Fourier-Mellin transform. While mutual information could be employed here, we choose instead to apply it to the lower dimension...

We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to the Mellin transform of the absorptive part of the amplitude. By inverting the transform, the absorptive part of the amplitude can be easily calculated. We ...

We present proofs for typical entries from the Gradshteyn-Ryzhik Table of Integrals using the Mellin transform method and computer algebra algorithms based on WZ theory. After representing an identity from the Table in terms of multiple contour integrals of Barnes’ type and nested sums, we use Wegschaider’s summation algorithm to find recurrences satisfied by both sides of this identity and che...

In this paper, we use Mellin transform to get the expression for the free boundary an price of an American finite-lived option, when the underlying is govern by the Levy process. We have also derived the free boundary and price of an American perpetual put as the limit of the preceded finite-lived option. We then show how to compute the price of an American option on a basket of stocks using Me...

We hear vowels pronounced by men and women as approximately the same although the length of the vocal tract varies considerably from group to group. At the same time, we can identify the speaker group. This suggests that the auditory system can extract and separate information about the size of the vocal-tract from information about its shape. The duration of the impulse response of the vocal t...

A new family of probability distributions βM,N , M = 0 · · ·N, N ∈ N on the unit interval (0, 1] is defined by the Mellin transform. The Mellin transform of βM,N is characterized in terms of products of ratios of Barnes multiple gamma functions, shown to satisfy a functional equation, and a Shintani-type infinite product factorization. The distribution log βM,N is infinitely divisible. If M < N...