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Optimization of Basic Magnetic Field Homogeneity in MR Tomography
Hadinec, Michal ; Brančík, Lubomír (referee) ; Frollo, Ivan (referee) ; Bartušek, Karel (advisor)
This thesis is concerned with problems of measuring and mapping of magnetic field in MR tomograph, for purpose of magnetic flux density homogeneity optimization. Attention is paid to mapping techniques on rotary symmetric volume and to ways of magnetic fields optimization with utilization of passive and active correction systems. Theoretical analysis of magnetic field decomposition with utilization of spherical harmonics and numerical decomposition is made. Mapping and approximation techniques of basic magnetic field are verified by experiments in the laboratory at the Institute of Scientific Instruments AS CR in Brno.
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Application of Legendre basis for spectral analysis
Mesárošová, Michaela ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
The thesis focuses on the possibilities of using Legendre polynomials in order to obtain a spectrum of signals. It examines their properties in the time and frequency domain such as generating methods, root position, and orthogonality. Another goal was to implement the Legendre transform and to verify the quality of the obtained spectra and signal approximations in comparison with various methods. Finally, it deals with the choice of a suitable approximation order as well as the analytical possibilities of spectrum calculation.
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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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Application of Legendre basis for spectral analysis
Mesárošová, Michaela ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
The thesis focuses on the possibilities of using Legendre polynomials in order to obtain a spectrum of signals. It examines their properties in the time and frequency domain such as generating methods, root position, and orthogonality. Another goal was to implement the Legendre transform and to verify the quality of the obtained spectra and signal approximations in comparison with various methods. Finally, it deals with the choice of a suitable approximation order as well as the analytical possibilities of spectrum calculation.
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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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Optimization of Basic Magnetic Field Homogeneity in MR Tomography
Hadinec, Michal ; Brančík, Lubomír (referee) ; Frollo, Ivan (referee) ; Bartušek, Karel (advisor)
This thesis is concerned with problems of measuring and mapping of magnetic field in MR tomograph, for purpose of magnetic flux density homogeneity optimization. Attention is paid to mapping techniques on rotary symmetric volume and to ways of magnetic fields optimization with utilization of passive and active correction systems. Theoretical analysis of magnetic field decomposition with utilization of spherical harmonics and numerical decomposition is made. Mapping and approximation techniques of basic magnetic field are verified by experiments in the laboratory at the Institute of Scientific Instruments AS CR in Brno.
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