We employ the Mellin transform to facilitate the bit error ratio (BER) analysis of a fast frequency hopping (FFH)-assisted, M -ary frequency-shift keying (MFSK) using product combining (PC) when the transmitted signal is subjected to both Rayleigh fading and partial-band noise jamming. Exploiting the fact that the Mellin transform of the product of independent random variables is the product of...

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure, not requiring exponential sampling, is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into...

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...

The infinite sums often encountered in thermal Feynman diagrams are commonly computed using the function coth, or one with similar properties, to generate poles in the complex plane whose residues correspond to the terms in the sum [1]. This transforms the summation into a contour integration and conveniently splits the zero-temperature and thermal contributions. The method ceases to be ideal w...

Human activity recognition is attracting a lot of attention in the computer vision domain. In this paper we present a novel human activity recognition method based on transform and Fourier Mellin Transform (FMT). Firstly, we convert the original image sequence to the Radon domain, get the transform curves by transform. Then we extract the Rotation-Scaling-Translation (RST) invariant features by...

A pattern descriptor invariant to rotation, scaling, translation (RST), and robust to additive noise is proposed by using the Radon, Fourier, and Mellin transforms. The Radon transform converts the RST transformations applied on a pattern into transformations in the radial and angular slices of the Radon transform data. These beneficial properties of the Radon transform make it an useful interm...

The “twisted Mellin transform” is a slightly modified version of the usual classical Mellin transform on L([0,∞)). In this short note we investigate some of its basic properties. From the point of view of combinatorics one of its most interesting properties is that it intertwines the differential operator, df/dx, with its finite difference analogue, ∇f = f(x)−f(x−1). From the point of view of a...

Many digital audio effects rely on transformations performed in the Fourier-transformed (frequency) domain. However, other transforms and domains exist and could be exploited. We propose to use the Mellin transform for a class of sound transformations. We present a fast implementation of the Mellin transform (more precisely a Fast Scale Transform), and we provide some examples on how it could b...

In this contribution we generalize the classical Fourier Mellin transform [3], which transforms functions f representing, e.g., a gray level image defined over a compact set of R. The quaternionic Fourier Mellin transform (QFMT) applies to functions f : R → H, for which |f | is summable over R+ × S under the measure dθ dr r . R ∗ + is the multiplicative group of positive and non-zero real numbe...