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Application of Generalized Laguerre Functions to System Identification and Modeling
Tůma, Martin ; Kozák,, Štefan (referee) ; STRAKA,, Ondřej (referee) ; Jura, Pavel (advisor)
Tato práce se zabývá použitím zobecněných Laguerrových funkcí pro modelování a identifikaci dynamických systémů. Po krátkém úvodu je uvedena definice zobecněných Laguerrových polynomů a funkcí a některé jejich vlastnosti. Je zavedena metoda pro identifikaci spojitých dynamických systémů z diskrétních nasamplovaných dat s použitím zobecněných Laguerrových funkcí a porovnána s metodou nejmenších čtverců. Je diskutována volba optimálních parametrů p a alpha pro konečné Fourierovy řady se zobecněnými Laguerrovými funkcemi. Na příkladech je porovnána navržená identifikační metoda s metodou nejmenších čtverců. Je zavedena diskrétní Laguerrova transformace a její rozšíření s použitím zobecněných Laguerrových funkcí. Na příkladech je předvedena aplikace diskrétní Laguerrovy transformace na kompresi dat. Je ukázáno, že použití diskrétní Laguerrovy transformace může vést k lepším výsledků při kompresi dat než tradiční postup s využitím diskrétní kosinové transformace.
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Fractional order LTI SISO systems modelling using generalized Laguerre functions
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.
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The use of fluid medium in forming technologies
Tůma, Martin ; Dvořák, Milan (referee) ; Peterková, Eva (advisor)
The aim of this work is recognition manufactoring methods making use liquid like forming media and estimation measurment their usage in present. Making summary of all methods, which make use liquid for manufacturing components. Further are here introduced examples of parts, which are used in practice, method used at their manufacturing and comparing advantages and hadicap in comparasion with conventional methods.
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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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Dead time LTI SISO systems approximation using generalized Laguerre functions
Zsitva, Norbert ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This final thesis deals with the approximation of time delay in time invariant systems. First, the generalized Laguerre functions and their characteristics are presented. After this, the approximation of the Dirac delta function with the help of these functions is shown. Also, the choice of the free parameters is discussed and the results are evaluated with the help of energy. In the final part of the thesis, the approximations of systems with generalized and simple Laguerre functions are compared.
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Application of the Hermite basis for spectral analysis
Mihálik, Ondrej ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
The work is concerned with an application of the Hermite functions in signal approximation. The purpose of the work is to show their properties in time and frequency domains, namely their orthogonality, Fourier transform, zeros and asymptotic behaviour as their order becomes high. The next subject of this work is the question of scaling these functions to minimize the square error of signal approximation. Several methods proposed by different authors are discussed. Finally these algorithms are tested by approximating simple signals so that their results can be compared.
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Belt conveyor for food corn
Tůma, Martin ; Malášek, Jiří (referee) ; Pokorný, Přemysl (advisor)
The aim of this thesis is to design an angled belt conveyor for transportation of food with the capacity of 95,000 kg per hour and axial distance between the drums at both ends of 28 meters and heigh difference of 7 meters. The thesis includes a description of the main part of the conveyor belt and functional calculation according to standart ČSN ISO 5048 and determination of main dimension and design of the drive and tensioning device of the conveyor. Is performed stress analysis driven drum and analysis of the properties of materials transported
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Concept of pilot project for plastics manufacturing
Tůma, Martin ; Orel, Daniel (referee) ; Kandus, Bohumil (advisor)
The aim of this thesis is design of technology project for plastic manufacturing. The theoretical part is focused on the characteristics of plastics and plastics production, especially for injection molding of thermoplastics. In the practical part are presented the calculations needed to choice of the injection molding machines and the capacity calculations to determine consumption of granulate and productivity of injection molding machines. Part of this thesis is a list of optimal machinery, including the required peripherals and handling devices complying with the current requirements of a modern plastic manufacturing. The result of this thesis is an economic evaluation of investment costs of machinery for small and medium-sized plastic manufacturing.
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Deleuze: Virtual Differential Fields and their Actualization
Tůma, Martin ; Petříček, Miroslav (advisor) ; De Santis, Daniele (referee)
This thesis is divided into two parts, each of which corresponds to a particular line of inquiry. The first asks about the general character of Deleuze's philosophy. What kind of philosopher is he? What are the chief defining features of his philosophy? How does his work fit into the larger context of the history of ideas? We proceed by discussing Deleuze's relation to some of his main influences, namely Plato, Nietzsche, and Kant, but also certain areas of mathematics, gradually sharpening our understanding of Deleuze's own views in the process. The second part then asks, against the background of this general characterization, after the specific form of Deleuze's ontology. What is the Deleuzian world like? What are its constitutive moments? What are the relations between these moments? We begin with the most general outline and gradually complicate it by introducing more of Deleuze's terminology. In particular, what interests us in this second part is Deleuze's concept of the virtual and his mechanism of immanent genesis through which psychical, biological, social, material, as well as all other forms come to be constituted, that is, the process of indi-different/ciation. In order to do this, we use Deleuze's relation to Kant to frame his ontological project, and rely on mathematics to ground the enquiry....
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