Search results for "Transform"

Rectifiability and singular integrals

1995

An Improved Method for Estimating the Time ACF of a Sum of Complex Plane Waves

2010

Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we pr…

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.

Carleson's counterexample and a scale of Lorentz-BMO spaces on the bitorus

2005

We introduce a full scale of Lorentz-BMO spaces BMO L p,q on the bidisk, and show that these spaces do not coincide for different values ofp andq. Our main tool is a detailed analysis of Carleson's construction in [C].

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…

Transformation of the Forest-based Bioeconomy by Embracing Digital Solutions

2017

This paper attempts to explore a new insight to both industrialized and growing economies by demonstrating a digital-driven creative disruption in the forest-based bioeconomy which is beginning to replace its conventional and narrow concept of a forest-blinded economy. Notwithstanding the potential broad cross-sectoral benefits to both industrialized and growing economies, natural environments and locality constraints and the incessant challenge of distance have impeded balanced development of this economy. However, driven by digital solutions the economy has taken big steps forward in recent years. Digitalization has enabled real-time end-to-end supply chain visibility, improved delivery a…

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…

Bridging authentic learning task into technology supported transformative pedagogy in Finnish teacher training

2018

The goal of the Finnish teacher training is to educate autonomous teachers, who have pedagogical competence and theoretical understanding about using ICT in teaching and learning. In this study, we describe teacher students’ pedagogical ICT competence as designers of technology supported learning tasks. The study is based on Hughes’ RAT model, which is a framework for assessing technology integration. The theoretical definition of RAT model is technology as a) replacement, b) amplification or c) transformation. To define this there are three systematical dimensions to analyze a particular technology use: Instructional Methods, Student learning processes and Curriculum Goals. The data consis…