|
|
Bandlimited signals, their properties and extrapolation capabilities
Mihálik, Ondrej ; Havránek, Zdeněk (referee) ; Jura, Pavel (advisor)
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.
|
|
|
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.
|
|
|
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.
|
|
|
Application of Chebyshev Basis for Spectral Analysis
Ettl, Ondřej ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
The work is focused on finding and verifying the basic properties of Chebyshev polynomials in Hilbert space. These include their generating functions, weight functions, orthogonality and recurrent relationships. Another goal was signal processing by Chebyshev’s transform and investigation of the resulting spectrum. Lastly the focus is shifted towards demostrain of two methods for modeling of frequency spectrum with help of Chebyshev polynomials.
|
|
|
Application of Chebyshev Basis for Spectral Analysis
Ettl, Ondřej ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
The work is focused on finding and verifying the basic properties of Chebyshev polynomials in Hilbert space. These include their generating functions, weight functions, orthogonality and recurrent relationships. Another goal was signal processing by Chebyshev’s transform and investigation of the resulting spectrum. Lastly the focus is shifted towards demostrain of two methods for modeling of frequency spectrum with help of Chebyshev polynomials.
|
|
|
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.
|
|
|
Bandlimited signals, their properties and extrapolation capabilities
Mihálik, Ondrej ; Havránek, Zdeněk (referee) ; Jura, Pavel (advisor)
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.
|
|
|
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.
|
guest ::
