Various methods of DNA sequences modifications for frequency analysis and basic characteristics of DNA are described in the theoretical part of this thesis. Tricolor spectrograms, created by short time Fourier transform help us to recognize some characteristic patterns in DNA sequences. Practical part of this work deals with developed programme which generates spectrograms and analyse them. Last part deals with the analysis of selected sequences of C. elegans genome. Some patterns are related to data of public databases such as NCBI. Various patterns are explained from the biological nature, which relates to chromosome structure and protein coding regions. Another well recognised patterns, tandem repetitions composed of satellites, microsatellites and minisatelites are described by spectrograms as well.

This thesis discusses about possibilities of construction colour DNA spectrograms and about patterns which can be detected there. Spectrograms as tools of spectral analysis give us a simultaneous view of the local frequency throughout the nucleotide sequence. They are suitable for gene identification or gene regions identification, determination of global character about whole chromosomes and also give us a chance for the discovery of yet unknown regions of potential significance. For purpose of this kind of DNA analysis is possible to use digital signal processing methods. We can apply them on only after conversion of DNA sequence to numerical representation. Selection of correct numerical representation affects how well will be reflected biological features in numerical record which we need for another use in digital signal analysis.

This diploma project is focused on use the fractals in diffractive optical elements. Properties of diffraction patterns of various fractals are investigated. Properties of some simpler non-fractal structures are investigated too. Diffraction patterns are created by computer with program written in Delphi programming language. Potentialities of use the fractals in security optical elements (holograms) and their advantages against the classic non-fractal structures.

The master's thesis focuses on vortical structures with cavitating core, which might develop in Francis turbines at non-optimal discharges in a form of unstable vortex cord. The cavitating vortex core is to be generated in a lab by flow rotation and a convergent nozzle. The objective of this thesis is to compare experimental results with mathematical model of pressure drop in vortical flow and with numerical calculation in Fluent based on finite volumes method. Other objective is to messure high frequency pressure vibrations generated by cavitating vortex core and spectrally analyze the data.

This master's thesis deals with phone call detection in recordings of radio broadcast data. I will introduce an approach, that will diarize broadcast record to segments with phone calls and segment where moderator speaks. Efficiency will be evaluated at frame level against manually annotated record.

The main subject of this work represents the time-frequency signal analysis. Firstly, it intends to provide the most essential theoretical background with focus on the continuous wavelet transform, where also a comparison of the key features with its close relative the short-time Fourier transform is performed. Afterwards, there follows a demonstration of the purpose with a practical example. The particular aim is to create a phase vocoder solution for modifying the length of a sound record duration and pitch shifting. Here, in this place, the functional principles, design, procedure of assembling, outputs and achieved results are well documented.

This thesis covers the basics in the stochastic homogenization of elliptic partial differential equations, from underlying theory up to numerical ap- proaches. In particular, we introduce and analyze a combination of the Fourier-Galerkin method in the spatial domain with a collocation method in the stochastic domain. The material coefficients are assumed to depend on a finite number of random variables. We present a comparison of the Monte Carlo method with the full tensor grid and sparse grid collocation method for two applications. The first one is the checkerboard problem with continuous random variables, the other considers the material coefficients to be described in terms of an autocorrelation function.

This thesis concerns the relations between correlation matrix, difference propagation matrix and other matrices used in the block cipher cryptanalysis. We show that some relations between these matrices can be seen just as a change of basis provided by the discrete Fourier transform. This can be used for an easier proof of a well-known theorem. We also study properties of difference propagation matrix, describe a class of vectorial Boolean functions which have the same difference propagation matrix and state a numerically justified hypothesis that this class contains all such functions.

The aim of the thesis is to focus on the different methods of analysis of vibration signals. Focusing on the physical fundamentals of vibrations and a description of their origin in an electrical machine. Describe the vibration sources from mechanical across the electromagnetic to the aerodynamic. Defining the current defects of electric machines and sensors suitable for the measurement of vibrations in an electric machines. Introduction to the methods of analysis of vibration signals in the time and frequency domain. Then using some of these methods for the analysis of vibration signals measured asynchronous motors with different manufacturer defined production defect. The conclusion is composed from the comparison between measured and analyzed results.

The goal of the thesis is to find general nonlinear geometric transformation, which compensates irregular deformation of images, so that they could be registered. In the introductory part, necessary mathematical tools are stated, especially convolution, correlation and Fourier transform. In the next part, method of phase correlation is stated, followed by algorithms used for finding the geometric transformation. Those algorithms are implemented in computer program, that is included.