Search results for "Fourier transform"

Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES

2005

In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…

Variable fractional Fourier processor: a simple implementation: erratum

1997

Random Walk and Diffusion

2014

The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.

Improved Quadratic Time-frequency Distributions for Detecting Inter-turn Short Circuits of PMSMs in Transient States

2020

This paper aims to improve quadratic time-frequency distributions to adapt condition monitoring of electrical machines in transient states. Short-Time Fourier transform (STFT) has been a baseline signal processing technique for detecting fault characteristic frequencies. However, limits of window sizes due to loss of frequency- or time-resolution, make it hard to capture rapid changes in frequencies. Within this study, Choi-Williams and Wigner-Ville distributions are proposed to effectively detect peaks at characteristic frequencies while still maintaining low computation time. The improved quadratic time-frequency distributions allow for generating spectrograms of a longer lasting data sig…

Detecting explosive substances by the IR spectrography

2014

Fast and safe detection methods of explosive substances are needed both before and after actualized explosions. This article presents an experiment of the detection of three selected explosives by the ATR FTIR spectrometer and by three different IR hyperspectral imaging devices. The IR spectrometers give accurate analyzing results, whereas hyperspectral imagers can detect and analyze desired samples without touching the unidentified target at all. In the controlled explosion experiment TNT, dynamite and PENO were at first analyzed as pure substances with the ATR FTIR spectrometer and with VNIR, SWIR and MWIR cameras. After three controlled explosions also the residues of TNT, dynamite and P…

Curvelet-based method for orientation estimation of particles from optical images

2014

A method based on the curvelet transform is introduced to estimate the orientation distribution from two-dimensional images of small anisotropic particles. Orientation of fibers in paper is considered as a particular application of the method. Theoretical aspects of the suitability of this method are discussed and its efficiency is demonstrated with simulated and real images of fibrous systems. Comparison is made with two traditionally used methods of orientation analysis, and the new curvelet-based method is shown to perform better than these tradi- tional methods. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of th…

Pressure-Dependent Tuning of Photoluminescence and Size Distribution of Carbon Nanodots for Theranostic Anticancer Applications

2020

Carbon nanodots (CDs) have recently attracted attention in the field of nanomedicine because of the biocompatibility, cost-effective nature, high specific surface, good near infrared (NIR) photothermal conversion into heat and tunable fluorescence properties, which have paved the way toward incorporating use of CDs into innovative anticancer theranostic platforms. However, a reliable synthesis of CDs with established and controlled physiochemical proprieties is precluded owing to the lack of full manipulation of thermodynamic parameters during the synthesis, thus limiting their use in real world medical applications. Herein, we developed a robust solvothermal protocol which allow fine contr…

Statistical Approximation of Fourier Transform-IR Spectroscopy Data for Zinc White Pigment from Twentieth-Century Russian Paintings

2017

We present a statistical model for approximation of experimental Fourier transform-IR spectroscopy (FTIR) data for paint samples from paintings of different ages. The model utilizes random variations in some parameters (initial ageing rate, degree of change in ageing rate and time at which the change occurs). We determine the parameters characterizing variation in the paint composition and the storage conditions for the paintings. The numerical calculation is qualitatively consistent with the experimental data. In the proposed model, changes in the initial composition of the paint and the storage conditions make about the same contribution to the experimentally observed scatter in the data …