The aim of this finish work is an analysis of selected demographic time series and calculation of their predictions. Concretely, it deals with time series of annual crude birth rate, crude death rate, and the average age of mothers at first birth, all for the time period of 1960-2013. First, demographic terms used further in the work are defined. There is also a theoretical part describing the statistical methods used, specifically the methodology of time series from authors Box-Jenkins. Developement of each time serie is evaluated socio-demographically and the procedure of selecting the most appropriate interpolation model and calculation of predictions derived from it are described. There is also description of a process of selecting a suitable model based on the extrapolation method of predictions with Rolling Origin, construction of predictions derived from it and their comparison with the most suitable interpolation model. At the end there is a comparison of the time series of crude birth rate between the Czech Republic and selected developed country (Sweden), which brings interesting results.

This thesis is interested in describing stationary random discrete signals, especially) in music discrete signals. Here is described when is signal stationary and when is not stationary. It contains tip for preprocessing of signal for accurate recognition of local stationarity. Thesis contain mathematical definition of parameters of random digital signals, which are used for stationarity recognition. It is followed by description of basic windows, their categories, describing of their parameters and comparing of each. In next part of thesis are described mothods of segmentations with constant window constant overlap save, constant window constant ovelap add, variable window constant overlap save, variable window constant ovelap add and variable window variable overlap add. It is followed by analyzing of windows used in segmentations with variable lengths of segments. As next point of thesis are transients made by step changes of coefficients of filter in filtering of segments with variable lengths. At the end is investigated the best accurate method of signal stationarity detection. Segments made by accurate method of detection are analyzed. thesis contains exapmle of music signal segmentation.

The emphasis of this diploma thesis is placed on the verification of stationarity in time series using the Unit Root Tests and their most common modifications that are introduced in the theoretical part of this paper. Tests mainly by Dickey and Fuller, Phillips and Perron, and KPSS test are introduced as well as their modifications in the form of ERS, Ng and Perron, and Leybourne and McCabe tests. Moreover the HEGY test for testing stationarity in the seasonal Time series and Perron test of structural breaks for Time series with shocks are described. There is also outlined the process of testing multiple Unit Roots. The empirical part of this paper consists of simulations of AR(1) time series generated using the software R, their testing for stationarity by selected Unit Root tests and the comparison of power of these tests. The conclusion includes recommendations which tests and under what conditions are the most suitable for testing Time series for the presence of Unit Root.

Master’s thesis deal about electroencefalography, measurement EEG signals and analysis measuermed signals. Project contains two basis practical parts. Firts part contain two PC’s programs that’s are used to fundamental analysis to frequence-domain and visual display of brain mapping created with Matlab. Second chapter of practical parts includes two PC’s programs created with LabView. First of them is the EEG biofeedback making use for advanced analyses and second program is used to detection segment of stacionarity.

This paper takes aim at creating a consistent form of study materials, supplemented with illustrative examples, for Signals and systems subject. The thesis starts with basic characteristics of acoustic, image, biological and communication signals. Characteristics of linear signals and AD&DA conversion has been added to the next part and to complete the submission, discrete signals follow. Diploma thesis as a whole contains basic theoretical description of problematics, which it tries to supplement with interesting examples, connections, graphs and matlab scripts for illustrative presentation of mentioned problematics.