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1

The heat equation on time scales

Cuchta Tom, Ferreira Rui A. C.

Opuscula Mathematica

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2023

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Vol. 43, no. 4

475--491

EN

We present the use of a Fourier transform on time scales to solve a dynamic heat IVP. This is done by inverting a certain exponential function via contour integral. We include some specific examples and directions for further study.

2

3D Synthetic Aperture Imaging Method in Spectrum Domain for Low-Cost Portable Ultrasound Systems

Tasinkiewicz Jurij

Archives of Acoustics

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2023

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Vol. 48, No. 4

559--572

EN

Portable, hand-held ultrasound devices capable of 3D imaging in real time are the next generation of the medical imaging apparatus adapted not only for professional medical stuff but for a wide group of less advanced users. Limited power supply capacity and the relatively small number of channels used for the ultrasound data acquisition are the most important limitations that should be taken into account when designing such devices and when developing the corresponding image reconstruction algorithms. The aim of this study was to develop a new 3D ultrasound imaging method which would take into account the above-mentioned features of the new generation of ultrasonic devices – low-cost portable general access scanners. It was based on the synthetic transmit aperture (STA) method combined with the Fourier spectrum domain (SD) acoustic data processing. The STA using a limited number of elements in transmit and receive modes for ultrasound data acquisition allowed both aforementioned constraints to be obeyed simultaneously. Moreover, the computational speed of the fast Fourier transform (FFT) algorithm utilized for the ultrasound image synthesis in the spectrum domain makes the proposed method to be more competitive compared to the conventional time domain (TD) STA method based on the delay-and-sum (DAS) technique, especially in the case of 3D imaging in real time mode. Performance of the proposed method was verified using numerical 3D acoustic data simulated in the Field II program for MATLAB and using experimental data from the custom design 3D scattering phantom collected by means of the Verasonics Vantage 256™ research ultrasound system equipped with the dedicated 1024-element 2D matrix transducer. The method proposed in this paper was about 80 times faster than its counterpart based on the time domain synthetic transmit aperture (TD-STA) approach in the numerical example of a single 3D ultrasound image synthesized from 4 partial images each containing 64 × 64 × 512 pixels. It was also shown that the acceleration of the image reconstruction was achieved at the cost of a slight deterioration in the image quality assessed by the contrast and contrast-to-noise ratio (CNR).

3

Spectral analysis for tilted fiber Bragg gratings in the corrosion detection for concrete structure

Kwong Kok Zee, Udos Waldo, Lim Kok-Sing, Lee Foo Wei, Tan Chee Ghuan, Samion Muhamad Zharif, Ahmad Harith

Optica Applicata

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2022

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Vol. 52, nr 3

429--439

EN

An effective corrosion monitoring technique is sought after by the engineers for assessing the steel bar corrosion at the early stage for the maintenance and repair works, especially in the corrosive environments, such as coastal and marine. In this work, tilted fiber Bragg grating (TFBG) with the optical sensor is employed in corrosion monitoring of a reinforced concrete structure. Taking advantage of the high sensitivity of TFBG cladding resonance wavelengths to the change in the surrounding medium, the sensor is mounted on the steel bar that is embedded in a concreted block during an accelerated corrosion process. The acquired transmission spectrum of the TFBG during the procedure is digitally processed using Fourier Transform to produce an index that is sensitive to the generated corrosion product surrounding the TFBG sensor. This eases the analysis of the sophisticated TFBG transmission spectra. The generated index can be used as an indicator (indicator J ) for the corrosion process of the embedded steel bar in the concrete structure. This indicator J can act as an indicator to describe the corrosion activity and corrosion level at a specific point of the steel bar in concrete structures.

4

Anatomical and functional assessment of patency of the upper respiratory tract in selected respiratory disorders - Part 2

Zając Andrzej, Kukwa Andrzej, Barański Robert, Nitkiewicz Szymon, Zomkowska Edyta, Rybak Adam

Metrology and Measurement Systems

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2022

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Vol. 29, nr 3

429--454

EN

This article presents selected physical diagnostic methods used in otorhinolaryngology and results of their application. In addition to the applications of methods using the capabilities of selective sensors, selected methods of hybrid diagnostics were also presented - for assessment of parameters of respiratory processes, with polysomnography as an example of using both typical diagnostic methods dedicated to otolaryngology, as well as standard EEG and ECG methods. It has been shown that in some special cases of respiratory disorders, measurements of the air flow in the respiratory tract can be supplemented with pressure measurements in selected positions within the airways. The presented optical methods and diagnostic systems are very often used in the diagnosis of diseases not specific for otolaryngology occurring in the area of the head and neck. The presented material is the second part of the study discussing both standard and widely used diagnostic methods. All presented methods are dedicated to otolaryngology. This text is a continuation of the material published in No 4 of 2021 [1].

5

Template Matching Using Improved Rotations Fourier Transform Method

Wijaya Marvin Chandra

International Journal of Electronics and Telecommunications

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2022

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Vol. 68. No. 4

881--888

EN

Template matching is a process to identify and localize a template image on an original image. Several methods are commonly used for template matching, one of which uses the Fourier transform. This study proposes a modification of the method by adding an improved rotation to the Fourier transform. Improved rotation in this study uses increment rotation and three shear methods for the template image rotation process. The three shear rotation method has the advantage of precise and noisefree rotation results, making the template matching process even more accurate. Based on the experimental results, the use of 10°angle increments has increased template matching accuracy. In addition, the use of three shear rotations can improve the accuracy of template matching by 13% without prolonging the processing time.

6

Optimization of gear teeth in the wind turbine drive train with gear contact’s uncertainty using the reliability-based design optimization

Lee Changwoo, Park Yonghui

Archive of Mechanical Engineering

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2022

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LXIX, nr 4

713--728

EN

Although gear teeth give lots of advantages, there is a high possibility of failure in gear teeth in each gear stage in the drive train system. In this research, the authors developed proper gear teeth using the basic theorem of gear failure and reliability-based design optimization. A design variable characterized by a probability distribution was applied to the static stress analysis model and the dynamics analysis model to determine an objective function and constraint equations and to solve the reliability-based design optimization. For the optimization, the authors simulated the torsional drive train system which includes rotational coordinates. First, the authors established a static stress analysis model which gives information about endurance limit and bending strength. By expressing gear mesh stiffness in terms of the Fourier series, the equations of motion including the gear mesh models and kinematical relations in the drive train system were acquired in the form of the Lagrange equations and constraint equations. For the numerical analysis, the Newmark Beta method was used to get dynamic responses including gear mesh contact forces. From the results such as the gear mesh contact force, the authors calculated the probability of failure, arranged each probability and gear teeth, and proposed a reasonable and economic design of gear teeth.

7

The method of determining the main harmonic frequency component

Szczepański Tomasz, Traczyk Stanisław, Dziedziak Paweł

Transport Samochodowy

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2021

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z. 1

38--42

EN

Analysis of vibroacoustic signals is one of the more frequently used diagnostic methods for mechanical devices occurring, among the others, in the car diagnostics. Often, it happens that the most important element of the recorded course is the fundamental harmonic frequency of vibrations. Fundamental frequency indicates the main process related to the operation of the device and allows to follow its course. In the article the author’s method of determining the fundamental frequency in the signal, being the subject of a patent application, will be presented. Its theoretical basis and application examples were discussed comparing the accuracy of its use with the accuracy of other methods. The frequency range where the method finds application is shown. That is, where its accuracy turns out to be better than the accuracy of popular methods used to determine fundamental harmonic frequency component.

PL

Analiza sygnałów wibroakustycznych jest jedną z częściej stosowanych metod diagnostycznych urządzeń mechanicznych, występującą między innymi w diagnostyce samochodowej. Często zdarza się, że najbardziej istotnym elementem rejestrowanego przebiegu jest główna składowa harmoniczna drgań. Dominująca częstotliwość świadczy bowiem o głównym procesie związanym z pracą urządzenia i pozwala śledzić jego przebieg. W artykule zostanie przedstawiona autorska metoda wyznaczania głównej częstotliwości występującej w sygnale, będąca przedmiotem zgłoszenia patentowego. Omówiono jej podstawy teoretyczne oraz przykłady zastosowania, porównując dokładność jej stosowania z dokładnością innych metod. Wskazano na zakres częstotliwości, gdzie metoda znajduje zastosowanie, to znaczy gdzie jej dokładność okazuje się lepsza, niż dotychczas stosowanych sposobów wyznaczania głównej składowej harmonicznej.

8

Introduction to Fourier analysis using IT tools of Laboratory of Technical Aids of Teaching IF UJ

Wietecha Tomasz, Kurzydło Piotr M., Bogacz Bogdan F.

Science, Technology and Innovation

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2021

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Vol. 12, no. 1

10--15

EN

The general aim of this article is to present didactic aspects of familiarizing students with the Fourier analysis. This didactic process issues through the use of IT tools of Laboratory of Technical Aids of Teaching is discussed. There are four separate computer stations, differing in software, where students learn step by step: composing signals from single harmonics, visualization through images of rotating vectors of harmonic signal composition, operation of a virtual generator of a given number of harmonics and elements of the CMA Coach system in the context of signal analysis. The applied didactic methods are aimed at students of biophysics for whom the Fourier analysis is of practical importance.

9

Anatomical and functional assessment of patency of the upper respiratory tract in selected respiratory disorders - Part 1

Kukwa Andrzej, Zając Andrzej, Barański Robert, Nitkiewicz Szymon, Kukwa Wojciech, Zomkowska Edyta, Rybak Adam

Metrology and Measurement Systems

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2021

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Vol. 28, nr 4

813--836

EN

The rapidly developing measurement techniques and emerging new physical methods are frequently used in otolaryngological diagnostics. A wide range of applied diagnostic methods constituted the basis for the review study aimed at presenting selected modern diagnostic methods and achieved diagnostic results to a wider group of users. In this part, the methods based on measuring the respiratory parameters of patients were analysed. Respiration is the most important and necessary action to support life and its effective duration. It is an actual gas exchange in the respiratory system consisting of removing CO2 and supplying O2. Gas exchange occurs in the alveoli, and an efficient respiratory tract allows for effective ventilation. The disruption in the work of the respiratory system leads to measurable disturbances in blood saturation and, consequently, hypoxia. Frequent, even short-term, recurrent hypoxia in any part of the body leads to multiple complications. This process is largely related to its duration and the processes that accompany it. The causes of hypoxia resulting from impaired patency of the respiratory tract and/or the absence of neuronal respiratory drive can be divided into the following groups depending on the cause: peripheral, central and/or of mixed origin. Causes of the peripheral form of these disorders are largely due to the impaired patency of the upper and/or lower respiratory tract. Therefore, early diagnosis and location of these disorders can be considered reversible and not a cause of complications. Slow, gradually increasing obstruction of the upper respiratory tract (URT) is not noticeable and becomes a slow killer. Hypoxic individuals in a large percentage of cases have a shorter life expectancy and, above all, deal with the consequences of hypoxia much sooner.

10

Fourier, Laguerre, Laplace Transforms with applications

Aghili Arman

Journal of Mathematics and Applications

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2021

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Vol. 44

5--17

EN

In this article, the author considered certain time fractional equations using joint integral transforms. Transform method is a powerful tool for solving singular integral equations, integral equation with retarded argument, evaluation of certain integrals and solution of partial fractional differential equations. The obtained results reveal that the transform method is very convenient and effective. Illustrative examples are also provided.

11

Analysis of solutions of the 1D fractional Cattaneo heat transfer equation

Siedlecka Urszula, Ciesielski Mariusz

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

87--98

EN

In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.

12

The method of obtaining the spectral characteristics of the scanning probe microscope

Kataieva Mariia, Kvasnikov Vladimir

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2021

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T. 11, nr 2

52--55

EN

The article discusses methods and algorithms for digital processing and filtering when carrying out nano-measurements using a scanning probe microscope. The paper discusses frequency methods for improving images, in particular, the use of the Fourier transforms with various filtering methods to improve the quality of the resulting image. Stable computational algorithms have been developed for transforming discrete signals based on the Fourier transform. Methods for the interpretation of the numerical results of the discrete Fourier transform in such packages as Matlab, MathCad, Matematica are presented. It is proposed to use a window transform, developed based on the Fourier transform, which makes it possible to single out the informative features of the signal and to reduce the influence of the destabilizing factors that arise when processing signals from a scanning gold microscope in real conditions.

PL

W artykule omówiono metody i algorytmy cyfrowego przetwarzania i filtracji podczas nano-pomiarów z wykorzystaniem mikroskopu z sondą skanującą. Badane są metody korekcji częstotliwości obrazu, w szczególności wykorzystanie transformaty Fouriera z różnymi metodami filtracji w celu poprawy jakości otrzymanego obrazu. Opracowano stabilne algorytmy obliczeniowe do konwersji sygnałów dyskretnych na podstawie transformaty Fouriera. Przedstawiono metody interpretacji numerycznych wyników dyskretnej transformaty Fouriera w takich pakietach jak Matlab, MathCad, Matematica. Proponuje się zastosowanie transformacji okienkowej opracowanej na podstawie transformaty Fouriera, która pozwala wyodrębnić charakterystykę informacyjną sygnału i zmniejszyć wpływ czynników destabilizujących występujących podczas przetwarzania sygnału z mikroskopu z sondą skanującą w warunkach rzeczywistych.

13

Ellipsometry based spectroscopic complex for rapid assessment of the Bi2Te3-xSexthin films composition

Kovalev Vladimir, Uvaysov Saygid, Bogucki Marcin

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2021

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T. 11, nr 4

67--74

EN

A comparative analysis of the current state and development of spectral ellipsometry (SE) is carried out, the main limitations typical of popular configurations of measuring devices are determined. An original technical solution is proposed that allows one to create a two-source SE that implements the ellipsometry method with switching orthogonal polarization states. The measuring setup provides high precision of measurements of ellipsometric parameters Ψand Δin the spectral range of 270–2200 nm and the speed determined by the characteristics of pulsed sources with a simple ellipsometer design.As objects for experimental researches, confirming the efficiency and high precision qualities of the fabricated SE, we used a GaAs/ZnS-quarter-wave device for a CO2laser and SiO2on Si calibration plates. The optical properties of Bi2Te3-xSexfilms were investigated in the range of 270–1000 nm using a multi-angle SE. It was shown that the optical properties of Bi2Te3-xSexfilms monotonically change depending on the ratio of selenium and tellurium.

PL

W artykule najpierw dokonano analizy porównawczej obecnego stanu rozwoju elipsometriispektroskopowej oraz określono główne ograniczenia typowe dla popularnych konfiguracji urządzeń pomiarowych. Zaproponowano oryginalne rozwiązanie techniczne pozwalające na stworzenie dwuźródłowego elipsometu spektroskopowego z przełączaniem ortogonalnych stanów polaryzacji. Układ pomiarowy zapewnia wysoką precyzję pomiarów parametrów elipsometrycznych Ψ i Δ w zakresie spektralnym 270–2200 nm i prędkości wyznaczonej przez charakterystyki źródeł impulsowych przy prostej konstrukcji elipsometru. Jako obiekty do badań eksperymentalnych potwierdzających wydajność i wysoką precyzję proponowanego elipsometu spektroskopowego, wykorzystano ćwierćfalowy przyrząd GaAs/ZnS dla lasera CO2oraz płytki kalibracyjne SiO2na krzemie. Właściwości optyczne warstw Bi2Te3-xSexzbadano w zakresie 270–1000 nm przy użyciu wielokątowego elipsometu spektroskopowego. Wykazano, że właściwości optyczne cienkich warstw Bi2Te3-xSexzmieniają się monotonicznie w zależności od stosunku zawartości selenu i telluru.

14

Tricopter vibration analysis

Popardovský Vladimír, Ferenčák Marek, Kriš Tomáš, Tomaštík Miroslav, Novotný Lukáš

Diagnostyka

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2021

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Vol. 22, No. 3

67--72

EN

Unmanned Aerial Vehicle (UAV) is exposed to various types of stress during flight. One of the most significant negative influences is the vibrations produced by the rotating parts. If we assume a UAV of the multicopter type, it is a stress of the whole structure by vibrations produced by propulsion units, which are placed on symmetrically distributed arms. The propulsion unit consists of an electric-propeller assembly, with the propeller being the largest source of vibration. This is due to the uneven distribution of the mass with respect to its axis of rotation. In addition to the propeller, the rotating part is also the electric motor itself, although the electric motor contributes much less to the total vibrations than the propeller. For this reason, it is necessary to balance the propeller first statically and then dynamically balance the entire drive unit (engine + propeller). Our work is focused on vibration diagnostics of an experimental tricopter in order to optimize the power units - to produce the smallest possible vibrations.

15

Identification and classification of selected internal combustion engine inefficiency based on vehicle structure vibrations

Prażnowski Krzysztof, Mamala Jarosław, Bieniek Andrzej, Graba Mariusz

Vibrations in Physical Systems

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2020

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Vol. 31, nr 1

art. no. 2020110

EN

The combustion engine generates forced vibrations, caused by periodically acting external forces resulting from the combustion of the fuel-air mixture. Any changes in this process cause an increase in the value of vibration amplitude and a change in the distribution of harmonics dominating in the frequency domain. In order to identify selected malfunctions of the internal combustion engine of the Polaris off-road vehicle tested, its current parameters were correlated with the vibrations transmitted to the vehicle's structural elements. An integrated sensor for measuring acceleration using the direct method, made in MEMS technology, was used for the tests. The recorded signals of the acceleration components were subjected to analysis in the frequency domain, thus identifying the characteristic harmonic components in the analyzed spectrum. For the classification of incompleteness based on registered signals, a diagnostic inference matrix based on our own algorithm of conduct was used.

16

General concept of the EMG controlled bionic hand

Pieprzycki Adam, Król Daniel

Science, Technology and Innovation

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2020

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Vol. 8, no. 1

26--34

EN

The article presents a general concept of a bionic hand control system using multichannel EMG signal, being under development at present. The method of acquisition and processing of multi-channel EMG signal and feature extraction for machine learning were described. Moreover, the design of the control system implementation in the real-time embedded system was discussed.

17

Comparison of Amplitude Variations of Seasonal and Sub-Seasonal Oscillations in Length of Day and Total Solar Irradiance

Kosek Wiesław, Gabryszuk Justyna

Journal of Ecological Engineering

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2020

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Vol. 21, nr 7

52--57

EN

The aim of the study was to identify and compute oscillations in two different time series with similar amplitude variations using length of day data with tide model removed (LODR) and total solar irradiance (TSI) data. The combination of the Fourier transform band pass filter and Hilbert transform allows detecting amplitude variations as a function of the oscillation period. The amplitude variations in two different time series enable computation of frequency dependent or time-frequency correlation coefficients between them. It allows also identifying such oscillations in two time series which have similar amplitude variations. The method applied to LODR and TSI data, enable to detect a possible relationship between them. This comparison method can be applied to any time series which consist of oscillations with non-constant amplitudes.

18

Analiza sygnałów w sieci energetycznej w paśmie wąskopasmowej transmisji PLC

Lisowiec Aleksander, Kalinowski Adam, Habrych Marcin, Michalski Paweł, Dąbkowski Paweł, Liżewska Anna, Zaklika Michał

Wiadomości Elektrotechniczne

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2019

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R. 87, nr 9

17--20

PL

Zakres częstotliwości od 3 kHz do 149 kHz jest używany w Europie do wąskopasmowej transmisji PLC. W artykule przedstawiono sposób oraz urządzenie do pomiaru sygnałów prądowych w sieci energetycznej niskiego napięcia w tym paśmie częstotliwości, w celu wykrywania zakłóceń transmisji PLC. Urządzenie składa się z układu akwizycji danych pomiarowych w postaci próbek sygnałów prądowych oraz oprogramowania zainstalowanego w komputerze PC do analizy sygnałów. Jako sensor prądowy zastosowano prądowy przetwornik bezrdzeniowy, pracujący na zasadzie cewki Rogowskiego.

EN

The frequency range from 3 kHz to 149 kHz is used in Europe for narrow-band PLC communication. In the paper the method and system for measuring the current signals in low voltage power line network have been described in order to detect the interference of narrow-band PLC transmission. The system consists of a data acquisition device and a software application installed on a PC computer. As a sensor an air-core current transducer working on Rogowski coil principle has been used.

19

Fourier Image Methods for Evolution Equations of Deep-Water Waves

Jankowski Jan, Leszczyński Henryk

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2019

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Vol. 23, No 3

261--268

EN

The velocity potential of the fluid satisfies the Laplace equation with nonlocal boundary conditions on a free surface. This differential problem is transformed to an evolution equation in Fourier variables. The Fourier transform images of boundary functions are approximated by Picard's iterations and the method of lines on meshes related to roots of Hermite polynomials. Due to convolutions of sine and cosine functions the integral terms of Picard's iterations reveal unexpected instabilities for wave numbers in a neighborhood of zero.

20

Modelling of a Wireless Channel with Time Dependent Parameters

Mieczyńska Marta, Borys Andrzej

Scientific Journal of Gdynia Maritime University

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2019

|

nr 111

24--38

EN

It is convenient to analyse wireless channels and links by exploiting their input-output description. This approach relies on treating the system as a black box, whose behaviour can be fully described by the relationship between the input and output signals. In this paper, we study a relationship of the above type for linear wireless channels having time-dependent parameters, which also takes a multipath propagation environment into account. A starting point for the derivations presented here is a relationship derived in the literature for this type of model with the application of a single sinusoidal input signal. The subject of this paper is the generalization of that relationship for periodic input signals and then of non-periodic signals. To the best of our knowledge, the literature lacks a suitably convincing generalization. The derivations of this paper exploit a principle of superposition valid for linear systems as well as the relations existing between Fourier series and the Fourier integrals. The discussion is illustrated by the results of simulations performed with the help of the MATLAB program.