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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Signály s omezeným spektrem, jejich vlastnosti a možnosti jejich extrapolace / Bandlimited signals, their properties and extrapolation capabilities

Mihálik, Ondrej January 2019 (has links)
The work is concerned with the band-limited signal extrapolation using truncated series of prolate spheroidal wave function. Our aim is to investigate the extent to which it is possible to extrapolate signal from its samples taken in a finite interval. It is often believed that this extrapolation method depends on computing definite integrals. We show an alternative approach by using the least squares method and we compare it with the methods of numerical integration. We also consider their performance in the presence of noise and the possibility of using these algorithms for real-time data processing. Finally all proposed algorithms are tested using real data from a microphone array, so that their performance can be compared.
2

Retrieval of Non-Spherical Dust Aerosol Properties from Satellite Observations

Huang, Xin 16 December 2013 (has links)
An accurate and generalized global retrieval algorithm from satellite observations is a prerequisite to understand the radiative effect of atmospheric aerosols on the climate system. Current operational aerosol retrieval algorithms are limited by the inversion schemes and suffering from the non-uniqueness problem. In order to solve these issues, a new algorithm is developed for the retrieval of non-spherical dust aerosol over land using multi-angular radiance and polarized measurements of the POLDER (POLarization and Directionality of the Earth’s Reflectances) and wide spectral high-resolution measurements of the MODIS (MODerate resolution Imaging Spectro-radiometer). As the first step to account for the non-sphericity of irregularly shaped dust aerosols in the light scattering problem, the spheroidal model is introduced. To solve the basic electromagnetic wave scattering problem by a single spheroid, we developed an algorithm, by transforming the transcendental infinite-continued-fraction-formeigen equation into a symmetric tri-diagonal linear system, for the calculation of the spheroidal angle function, radial functions of the first and second kind, as well as the corresponding first order derivatives. A database is developed subsequently to calculate the bulk scattering properties of dust aerosols for each channel of the satellite instruments. For the purpose of simulation of satellite observations, a code is developed to solve the VRTE (Vector Radiative Transfer Equation) for the coupled atmosphere-surface system using the adding-doubling technique. An alternative fast algorithm, where all the solid angle integrals are converted to summations on an icosahedral grid, is also proposed to speed-up the code. To make the model applicable to various land and ocean surfaces, a surface BRDF (Bidirectional Reflectance Distribution Function) library is embedded into the code. Considering the complimentary features of the MODIS and the POLDER, the collocated measurements of these two satellites are used in the retrieval process. To reduce the time spent on the simulation of dust aerosol scattering properties, a single-scattering property database of tri-axial ellipsoid is incorporated. In addition, atmospheric molecule correction is considered using the LBLRTM (Line-By-Line Ra- diative Transfer Model). The Levenberg-Marquardt method was employed to retrieve all the interested dust aerosol parameters and surface parameters simultaneously. As an example, dust aerosol properties retrieved over the Sahara Desert are presented.
3

Development of analytical solutions for quasistationary electromagnetic fields for conducting spheroids in the proximity of current-carrying turns.

Jayasekara, Nandaka 04 January 2013 (has links)
Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.
4

Development of analytical solutions for quasistationary electromagnetic fields for conducting spheroids in the proximity of current-carrying turns.

Jayasekara, Nandaka 04 January 2013 (has links)
Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.
5

A Quaternionic Version Theory related to Spheroidal Functions

Leitão da Cruz Morais, João Pedro 11 January 2023 (has links)
In dieser Arbeit wird eine neue Theorie der quaternionischen Funktionen vorgestellt, welche das Problem der Bestapproximation von Familien prolater und oblater sphäroidalen Funktionen im Hilberträumen behandelt. Die allgemeine Theorie beginnt mit der expliziten Konstruktion von orthogonalen Basen für Räume, definiert auf sphäroidalen Gebieten mit beliebiger Exzentrizität, deren Elemente harmonische, monogene und kontragene Funktionen sind und durch die Form der Gebiete parametrisiert werden. Eine detaillierte Studie dieser grundlegenden Elemente wird in dieser Arbeit durchgeführt. Der Begriff der kontragenen Funktion hängt vom Definitionsbereich ab und ist daher keine lokale Eigenschaft, während die Begriffe der harmonischen und monogenen Funktionen lokal sind. Es werden verschiedene Umwandlungsformeln vorgestellt, die Systeme harmonischer, monogener und kontragener Funktionen auf Sphäroiden unterschiedlicher Exzentrizität in Beziehung setzen. Darüber hinaus wird die Existenz gemeinsamer nichttrivialer kontragener Funktionen für Sphäroide jeglicher Exzentrizität gezeigt. Der zweite wichtige Beitrag dieser Arbeit betrifft eine quaternionische Raumfrequenztheorie für bandbegrenzte quaternionische Funktionen. Es wird eine neue Art von quaternionischen Signalen vorgeschlagen, deren Energiekonzentration im Raum und in den Frequenzbereichen unter der quaternionischen Fourier-Transformation maximal ist. Darüber hinaus werden diese Signale im Kontext der Spektralkonzentration als Eigenfunktionen eines kompakten und selbstadjungierteren quaternionischen Integraloperators untersucht und die grundlegenden Eigenschaften ihrer zugehörigen Eigenwerte werden detailliert beschrieben. Wenn die Konzentrationsgebiete beider Räume kugelförmig sind, kann der Winkelanteil dieser Signale explizit gefunden werden, was zur Lösung von mehreren eindimensionalen radialen Integralgleichungen führt. Wir nutzen die theoretischen Ergebnisse und harmonische Konjugierten um Klassen monogener Funktionen in verschiedenen Räumen zu konstruieren. Zur Charakterisierung der monogenen gewichteten Hardy- und Bergman-Räume in der Einheitskugel werden zwei konstruktive Algorithmen vorgeschlagen. Für eine reelle harmonische Funktion, die zu einem gewichteten Hardy- und Bergman-Raum gehört, werden die harmonischen Konjugiert in den gleichen Räumen gefunden. Die Beschränktheit der zugrundeliegenden harmonischen Konjugationsoperatoren wird in den angegebenen gewichteten Räumen bewiesen. Zusätzlich wird ein quaternionisches Gegenstück zum Satz von Bloch für monogene Funktionen bewiesen. / This work presents a novel Quaternionic Function Theory associated with the best approximation problem in the setting of Hilbert spaces concerning families of prolate and oblate spheroidal functions. The general theory begins with the explicit construction of orthogonal bases for the spaces of harmonic, monogenic, and contragenic functions defined in spheroidal domains of arbitrary eccentricity, whose elements are parametrized by the shape of the corresponding spheroids. A detailed study regarding the elements that constitute these bases is carried out in this thesis. The notion of a contragenic function depends on the domain, and, therefore, it is not a local property in contrast to the concepts of harmonic and monogenic functions. Various conversion formulas that relate systems of harmonic, monogenic, and contragenic functions associated with spheroids of differing eccentricity are presented. Furthermore, the existence of standard nontrivial contragenic functions is shown for spheroids of any eccentricity. The second significant contribution presented in this work pertains to a quaternionic space-frequency theory for band-limited quaternionic functions. A new class of quaternionic signals is proposed, whose energy concentration in the space and the frequency domains are maximal under the quaternion Fourier transform. These signals are studied in the context of spatial-frequency concentration as eigenfunctions of a compact and self-adjoint quaternion integral operator. The fundamental properties of their associated eigenvalues are described in detail. When the concentration domains are spherical in both spaces, the angular part of these signals can be found explicitly, leading to a set of one-dimensional radial integral equations. The theoretical framework described in this work is applied to the construction of classes of monogenic functions in different spaces via harmonic conjugates. Two constructive algorithms are proposed to characterize the monogenic weighted Hardy and Bergman spaces in the Euclidean unit ball. For a real-valued harmonic function belonging to a Hardy and a weighted Bergman space, the harmonic conjugates in the same spaces are found. The boundedness of the underlying harmonic conjugation operators is proven in the given weighted spaces. Additionally, a quaternionic counterpart of Bloch’s Theorem is established for monogenic functions.

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