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1

On Derivation of Discrete Time Fourier Transform from Its Continuous Counterpart

Borys Andrzej

International Journal of Electronics and Telecommunications

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2020

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Vol. 66, No. 2

355-360

EN

This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.

2

Thermal disturbances in twinned orthotropic thermoelastic material

Rani L., Singh V.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 4

897--910

EN

This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.

3

A proof of non-existence of self-imaging phenomenon in the incoherent case

Mamczur J. A.

Physics for Economy

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2017

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Vol. 1, No. 1

35-39

EN

The existing description of incoherent wave field propagation in terms of Fourier transformation has made possible to prove non-existence of the self-imaging phenomenon for incoherent images.

PL

Na podstawie istniejącego opisu optycznej propagacji niekoherentnych pól falowych z zastosowaniem transformacji Fouriera udowodniono teoretycznie nieistnienie zjawiska samoobrazowania dla niekoherentnych obrazów.

4

Ostre funkcje Fouriera Fsin i Fcos : zastosowanie w modelowaniu ciągów obserwacyjnych

Adamczewski Z.

Przegląd Geodezyjny

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2014

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R. 86, nr 11

3--7

PL

Autor przedstawia modele matematyczne szczególnego typu ciągu obserwacji. Wybrano dwa szeregi trygonometryczne Fouriera i po odpowiedniej parametryzacji nazwano je „ostrym sinusem Fouriera” Fsin i „ostrym cosinusem Fouriera” Fcos. Algorytmy oparte na tych funkcjach zostały poddane testom numerycznym. Algorytm modelu Fcos został też zastosowany do modelowania kilku zaobserwowanych ciągów czasowych obserwacji wskaźnika zawartości pary wodnej w troposferze IPW (Integrated Precipitable Water) podanych w pracy M.Kruczek [2]. Po zestawieniu wyników modelowania Autor przekazuje kilka uwag metodologicznych i praktycznych, dotyczących opracowania tego typu zbiorów obserwacji.

EN

The author presents mathematical models of observation series of a special type. Two trigonometric Fourier series have been selected. After relevant parametrisation they were called "the sharp Fourier sine" and "the sharp Fourier cosine". Algorithms based on those functions were then numerically tested. The algorithm of the Fcos model was also applied for modelling several series of temporal observations of an indicator of the steam in the troposphere (IPW - Integrated Precipitable Water); they are discussed in [2]. After presentation of modelling results the author discusses some methodological and practical aspects concerning processing series of observations of this type.

5

Układ sortujący obiekty na podstawie rozpoznawania kształtów

Sokołowski A.

Autobusy : technika, eksploatacja, systemy transportowe

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2013

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R. 14, nr 3

1269-1273

PL

W pracy przedstawiony został projekt urządzenia sortującego obiekty na podstawie ich kształtu. Proces sortowania odbywa się z wykorzystaniem wybranych transformacji całkowych, tutaj z wykorzystaniem transformacji Fouriera. Urządzenie sterowane jest z wykorzystaniem systemu ekspertowego.

EN

There is presented object sorting system in the paper. System is working on the base of shapes recognition. Sorting process is taking place with use of integral transformations, here with help of Fourier transforms. The device is controlled with help of expert system.

6

Detecting epileptogenesis in power variant domains

Lewis R. A., Parks B., Shmueli D., Capinst S.

Control and Cybernetics

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2011

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Vol. 40, no 2

293-314

EN

This paper presents the merging of two sets of experiments in the continuing endeavor to mine epileptiform activity from Electroencephalograms (EEG). The goal is to develop robust classification rules for identifying epileptiform activity in the human brain. We present advancements using the author's proprietary developed spectral analysis software to link power spectra of rat EEGs experiencing epilepsy seizures with the authors DFA algorithm and their MATLAB spectral analysis. Our system links 1) power spectra of seizures, in sleep, spike and seizure states, with 2) Deterministic Finite Automata (DFA). Combining power spectra with DFA to correctly predict and identify epileptiform activity (spikes) and epileptic seizures opens the door to creating classifiers for seizures. We also present a DFA that separates the states between seizure and nonseizure using robust testing and additional algorithms to increase the rigor when the methodology analyses noisy signals. Our results show optimal identification of seizures even when significant artifact and noise is present in the polyphonic domain. Herein we present a dual methodology that increases epileptoid identification in a noisy domain that links time and frequency domain components from MATLAB and proprietary software to clinical epileptiform activity.

7

Mikroskopia bliskiego pola Shear Force/sił atomowych z interpretacją wyników poddanych transformacie FFT

Sikora A., Gotszalk T., Szeloch R. F., Serafińczuk J., Jóźwiak G.

Elektronika : konstrukcje, technologie, zastosowania

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2008

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Vol. 49, nr 11

220-222

PL

W pracy zaprezentowano wstępne wyniki prac związanych z wykorzystaniem mikroskopii Shear Force do diagnostyki powierzchni. W metodzie tej ostrze skanujące wprawiane jest w drgania równolegle do powierzchni w częstotliwością bliską rezonansu, a następnie mierzona jest amplituda tych oscylacji w celu określenia odległości ostrza od powierzchni. Należy podkreślić fakt, iż ostrze znajduje się w odległości kilku-kilkunastu nanometrów od powierzchni, przez co metodę tą można zakwalifikować jako bezkontaktową. Do wykonania badań wykorzystano stanowisko własnej konstrukcji. Dodatkowo, technika detekcji oddziaływań bliskiego pola Shear Force połączona została z funkcją pomiaru prądu emisji z powierzchni skanowanej, co umożliwiło tworzenie map właściwości elektrycznych próbki. Przeprowadzenie dwuwymiarowej transformaty FFT pozwoliło na zaprezentowanie nowego sposobu analizy wyników pomiarów.

EN

The Shear Force Microscopy (SHFM) and some preliminary results of the surface measurements are presented. In this technique the tip oscillates laterally to the surface near one of its resonant frequencies and the tip's oscillation amplitude is measured in order to estimate the tip-sample distance. It must be emphasized that the tip maintains the distance of several nanometers from the surface; thereby this method can be classified as non-contact. The home-made instrument was used to perform the experiments. Additionally, the Shear Force technique was combined with surface emission measurement feature, which allowed to create a "map" of electrical surface properties. By performing the FFT transforms of the results, new analysis approach was presented.

8

On functions with Fourier transforms in Alip/p(G)

Aydin I., Sagir B.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

425-432

EN

Let G be a metrizable locally compact Abelian group with dual group G. [...] denotes the vector space of all complex-valued functions in L1 (G) whose Fourier transforms [...] belong to LP(G). Research on the spaces Ap(G) was initiated by Warner in [14] and Larsen, Liu and Wang in [7], Martin and Yap in [8]. Let Lip(alpha,p) and lip(alpha,p) denote the Lipschitz spaces defined on G. In the present paper, the space Alip/p(G) consisting of all complex-valued functions [...] whose Fourier transforms [...] belong to Lp(G) is investigated. In the first section invariant properties and asymptotic estimates for the translation and modulation operators are given. Furthermore it is showed that space App(G) is homogeneous Banach space. At the end of this work, it is proved that the space of all multipliers from L1 (G) to Alip/p(G) is the space Alip/p(G).

9

Elastodynamics of time harmonic inclined load in micropolar thermoelastic medium possessing cubic symmetry

Kumar R., Ailawalia P.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 3

629-644

EN

The analytic expressions for the displacements, microrotation, stresses and temperature distribution on the free surface of a micropolar thermoelastic medium possessing cubic symmetry as a result of time harmonic inclined load have been obtained. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The Fourierer transform has been employed to solve the problem. The variations of the displacements, microrotation, stresses and temperature distribution with the horizontal distance have been shown graphically.

10

Disturbance due to mechanical and thermal sources in orthorhombic thermoelastic material

Kumar R., Rani L.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 3

677-692

EN

A dynamical two-dimensional problem of thermoelasticity has been considered to investigate the disturbance due to mechanical (horizontal or vertical) force and thermal source in a homogeneous, thermally conducting orthorhombic material. The Fourier transforms are applied to basic equations to fonn a vector matrix differential equation, which is then solved by eigenvalue approach. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for the zinc crystal-like material are illustrated to show the comparison for various sources for the theory of coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) for an insulated boundary and temperature gradient boundary.

11

Filtering of Industrial Data using the Artifficial Neural Networks

Stanisławczyk A., Talar J., Jarosz P., Kusiak J.

Computer Methods in Materials Science

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2007

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Vol. 7, No. 2

311-316

EN

The data sets, which describe the parameters of any real industrial process, are usually noisy and often not complete. Moreover, the analysis of the data sets is complicated because of the measurement noise of different kinds. The filtering process of the data with the imposed noise is a complex problem and it is difficult to find appropriate general filtering method, which gives the reliable results. Sometimes, the filtering procedure eliminates important information, and sometimes leaves the unnecessary noise. This situation causes many problems with the gathering of the data, which can be useful in modelling of the considered industrial process. The main objective of the work is elaboration of the filtering procedures of the data sets obtained from the copper flash smelting process. The filtered data will serve to work out the Artificial Neural Network based control system of the copper flash smelting process. The existing models of that process are very simplified or based on the FEM models [1-4]. These models are useless from the point of view of the control system, because of its low accuracy and a long computation time. The idea of the control system of the copper flash smelting process is based on the artificial neural networks model [5,6]. The registered in the industrial conditions data are not suitable for the further analysis and modelling of the process. Therefore, the elaboration of the model must be preceded with the filtering of the data. Different techniques were applied to filtering of the noisy industrial data: Fourier Transform Method and techniques based on the Artificial Neural Networks. The filtered data sets were used to creation of the ANN model of the copper flash smelting process. The paper presents the results of filtering of the industrial data and the results of prediction of the chosen parameters of the copper flash smelting process using ANN model elaborated on the base of filtered data.

PL

W procesie modelowania obiektów przemysłowych często napotyka się na trudności związane ze specyfikacją i sposobem akwizycji danych opisujących rzeczywisty obiekt. Rejestrowane dane są zaszumione oraz często niekompletne. Również nie wszystkie istotne parametry mogą być rejestrowane. Filtrowanie danych z nakładającymi się szumami oraz zakłóceniami jest bardzo złożonym problemem, a znalezienie uniwersalnej metody filtrowania, która dawałaby wiarygodne rezultaty jest zadaniem skomplikowanym. Czasem procedury filtrowania eliminują istotne informacje, innym razem pozostawiają zbędny szum. Dlatego też, rejestrowane dane są często nieużyteczne dla dalszej analizy i modelowania procesu. Celem pracy jest prezentacja opracowanej procedury filtrowania, która pozwala na eliminowanie tych komponentów sygnałów wyjściowych, które nie mogą być przewidywane na podstawie rejestrowanych sygnałów wejściowych. Zaproponowany algorytm filtrowania danych wykorzystuje zalety różnych technik: filtrów adaptacyjnych, metody transformaty Fouriera oraz technik opartych o sztuczne sieci neuronowe. Opisano metodę filtrowania danych przemysłowych oraz zaprezentowano zastosowanie jej do filtrowania danych pochodzących z pieca do zawiesinowego wytopu miedzi.

12

The planar crack problem for a dielectric medium in a uniform electric field

Shindo Y., Narita F.

Archives of Mechanics

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2004

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Vol. 56, nr 6

447-463

EN

The theory for dielectric materials is applied to solve the planar problem of a Griffith crack in an infinite isotropic dielectric body subjected to a far-field tension and a uniform electric field. Fourier transforms are used to reduce the mixed boundary value problem to two simultaneous dual integral equations. The integral equations are then solved exactly, and the stress intensity factor and energy release rate under Mode I and Mode II loadings are expressed in closed form.

13

Penny-shaped crack in a piezoceramic cylinder under Mode I loading

Narita F., Lin S., Shindo Y.

Archives of Mechanics

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2003

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Vol. 55, nr 3

275-304

EN

The electroelastic response of a penny-shaped crack in a piezoelectric cylinder of finite radius is investigated in this study. Fourier and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. They are then reduced to a Fredholm integral equation of the second kind. Numerical values of the stress intensity factor, energy release rate and energy density factor for piezoelectric ceramics are obtained to show the influence of applied electrical loads.

14

Multi-loop linear control systems design

Goncharov V., Barkovsky A., Blinova N., Datsko O.

Systems Science

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2002

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Vol. 28, nr 4

5-16

EN

A numerical synthesis method of continuous control systems having few internal loops is proposed. Every loop may contain the correcting devices both in the direct channel and in the feedback circuit. The basis of the method is a real integral transform allowing writing the synthesis equation in the image domain in such a way that it contains the functions of real argument only. The interpolation approach provides the development of synthesis equations for the unknown coefficients of correcting device transfer functions. The system solution by Newton's method is found.

15

Influence and Green's functions for orthotropic micropolar continua

Kumar R., Choudhary S.

Archives of Mechanics

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2002

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Vol. 54, nr 3

185-198

EN

The article reports on a methodology to synthesize the response of orthotropic micropolar half-space subjected to concentrated and distributed loads. The disturbance due to normal and tangential loads are investigated by employing the eigenvalue approach. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential couple stress in the physical domain. The results concerning these quantities are given and illustrated graphically.

16

Fourier transforms of colour images : the quaternion FFT

Sangwine S.

Image Processing & Communications

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1998

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Vol. 4, no 1-2

3-8

EN

A discrete two-dimensional Fourier transform is presented, based on quaternion numbers (a generalisation of the complex numbers with three imaginary components). This transform allows a colour image in, say, RGB format, to be transformed as a whole, rather than as separate color components. Quaternion numbers are briefly reviewed, the transform is defined, and its two-dimensional cosinusoidal basis functions. The paper concludes with a discussion of a known problem with the transform : that a reversed image does not have a conjugate transform.