|
|
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 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.
|
|
|
Demystifying Band-Limited Extrapolation
Mihálik, Ondrej
Extrapolation of band-limited signals gained scientific attention over the last 60 years. Thefamous methods: Gerchberg-Papoulis algorithm, Prolate spheroidal wave functions (PSWFs), andsinc interpolation—they all promise excellent results. But when it comes to their practical implementation,users may find themselves struggling with many unanswered questions. Especially PSWFsbecame viewed as mysterious. They are hard to compute and even harder to apply. In theory theypromise excellent extrapolation capabilities—something which is contrary to our intuition. This paradoxis resolved if we admit that the real-world data contain noise. In this paper we review the abovementionedmethods and try to provide a brief assessment of their capabilities by considering theeffects of noise and the length of signal observation.
|
|
|
Reconstruction Of Non-Uniformly Sampled Signals Using Gerchberg-Papoulis Method
Mihálik, Ondrej
Analysis of non-uniformly sampled signals is often severely limited, since most signal processing methods rely on constant sampling period. If we still want to apply these methods, the signal must be resampled. Gerchberg-Papoulis algorithm is a method of signal reconstruction. It is commonly used for band-limited extrapolation of uniformly sampled data. We show that it is suitable for reconstruction of non-uniformly sampled signals as well. Our target application is reconstruction of time series measured by a car driving simulator. To demonstrate the benefits of band-limited reconstruction, we compare it with standard interpolation methods. The main advantage of the proposed algorithm is its ability to deal with noise and sampling jitter.
|
|
|
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.
|
guest ::
