This paper presents a novel kind of speech feature which is the modified Mellin transform of the log-spectrum of the speech signal (short for MMTLS). Because of the scale invariance property of the modified Mellin transform, the new feature is insensitive to the variation of the vocal tract length among individual speakers, and thus it is more appropriate for speaker-independent speech recognit...

A paper currency recognition system has a wide range of applications such as self receiver machines for automated teller machines and automatic good-selling machines. In this paper a new paper currency recognition system based on Fourier-Mellin transform, Markovian characteristics and Support Vector Machine (SVM) is presented. In the first, a pre-processing algorithm by Fourier-Mellin transform...

My assignment is going to introduce the Mellin transform and its application on harmonic sums [1]. Hjalmar Mellin(1854-1933, [2] for a summary of his works) gave his name to the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. Mellin transform is useful to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete prob...

New type Paley–Wiener theorems for the modified multidimensional Mellin and inverse Mellin transforms are established. The supports of functions are described in terms of their modified Mellin (or inverse Mellin) transform without passing to the complexification.

Using the Mellin transform a new method for solving the Black-Scholes equation is proposed. Our approach does not require either variable transformations or solving diffusion equations.

Modeling of the full temporal behavior of photons propagating in diffusive materials is computationally costly. Rather than deriving intensity as a function of time to fine sampling, we may consider methods that derive a transform of this function. To derive the Fourier transform involves calculation in the (complex) frequency domain and relates to intensity-modulated experiments. We consider i...

We describe how the extension of a solver for linear differential equations by Kovacic's algorithm helps to improve a method to compute the inverse Mellin transform of holonomic sequences. The method is implemented in the computer algebra package HarmonicSums.

The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe the Lévy stable distributions, and more generally the probability distributions governed by generalized diffusion equations of fractional order in space and/or in time. In these cases the related stochast...

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy proc...

A fast algorithm for the discrete-scale (and β-Mellin) transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, β-M...