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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 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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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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|
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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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