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Band-Limited Signal Extrapolation Using Least Squares Approximation By Prolate Spheroidalwave Functions
Mihálik, Ondrej
This paper is concerned with the band-limited signal extrapolation using a truncated series of Prolate spheroidal wave functions. 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. We briefly discuss performance of these two methods in the presence of noise and the possibility of using this algorithm for real-time data processing. Finally the extrapolation algorithm is tested with real data from a microphone array.
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Restoration of damaged audio signals using autoregressive models
Soboňa, Matúš ; Rajmic, Pavel (referee) ; Mokrý, Ondřej (advisor)
The bachelor thesis deals with the problem of restoring audio signals damaged by sample loss, using autoregressive models. The restoration itself is solved by W. Etter and A. Janssen's algorithms. These algorithms are implemented in MATLAB and tested on artificial signals aswell as on real recordings. Algorithms are then compared based on quality of restoration dependent on different parameters of signals.
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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.
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Image extrapolation methods
Ješko, Petr ; Špiřík, Jan (referee) ; Rajmic, Pavel (advisor)
The thesis deals with addition of pixels outside the image. Lists some methods for inpainting using computers and highlights the pitfalls that appear here. Examines methods for interpolation and approximation of functions in order to find the best method for extrapolating the image beyond its borders. Describes the basics of Wavelet transformation and Multiresolution analysis. It is proposed several methods for replenishment of pixels outside the image. PSNR and SSIM are used to compare achieved results. These methods are explained and compared. Briefly discusses the algorithm OMP, falling within the sparse representation of signals, and used in one of the methods. Also discussed is the development environment of MATLAB as a tool for the implementation of algorithms that practically solves the given problem. The practical part describes the implemented methods for adding pixels outside the image.
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Evaluation of behavioral insights with its aplication in the Czech Republic
Makovec, Petr ; Cingl, Lubomír (advisor) ; Štěpánek, Pavel (referee)
Implementing behavioral insights into policy making goes along well with widespread effort for increased efficiency. From the public budget administrator point of view, this efficiency is crucial since it directly affects the current state of the budget. The theoretical part of this thesis consists of description of the most important parts of behavioral economics that can be used during the creation and setting of public policies. It also consists of brief description of current behavioral insights teams that are already using the insights representing more realistic behavior and decision making of individuals. In the analytical part of this thesis, I provide methodology of experiment evaluation as well as result extrapolation facets and risks. Those experiments usually take place before any reasonable extension is made. I also provide financial analysis of several experiments, should they be extended to larger group of individuals. In the last chapter of the analytical part, I discuss the possibilities of implementation of behavioral economics in the Czech Republic. Based on the calculations I ran, even a small change of the environment where people make decisions can significantly improve the results of the intervention, all that with minimal costs. It is however important to point out that not all behavioral insights inspirations end with success. Application of behavioral insights into policy making has got a great potential when it comes to the Czech Republic, as I show Using two examples from Health care and taxes revenues.
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Evolution as a Way to God in the Work of Teilhard de Chardin
Jirousová, Františka ; Karfíková, Lenka (advisor) ; Sokol, Jan (referee) ; Macek, Petr (referee)
This dissertation deals with the notion of centration in the work of Teilhard de Chardin, the notion being examined with regard to two related aims: 1) to illustrate the logical structure of Teilhard's Christian theory of evolution, and 2) to explain the relation between centration carried out by created beings and centration assigned to God as the focal point of evolution. In other words: to explore the connection between fundamental freedom attributed by Teilhard to created beings and culminating in human beings according to him, and God's freedom demonstrating itself in controlling the universe and directing it to a goal being the fullness of being (pleroma). The first part presents Teilhard's life and the contexts of his work. The second part explains the main notions of Teilhard's theory and metaphysics, such as "consciousness", "spirit", "energy", "centro-complexity", and "matter", and relates them to the notion of centration. Centration is presented here as an activity of the consciousness consisting in the unifying formation of multitude by its interconnection with different types of relations around one centre. In such unification, the main law of evolution manifests itself - the Law of Differentiating Unity. This means that parts unified in such way start differentiating again. What is...
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Updating the Ultimate Forward Rate over Time: a Possible Approach
Žigraiová, Diana ; Jakubík, Petr
This study proposes a potential methodological approach to be used by regulators when updating the Ultimate Forward Rate (UFR) for the evaluation of insurers’ liabilities beyond the last liquid point observable in the market. Our approach is based on the optimisation of two contradictory aspects – stability and accuracy implied by economic fundamentals. We use U.S. Treasury term structure data over the period 1985-2015 to calibrate an algorithm that dynamically revises the UFR based on the distance between the value implied by the long-term growth of economic fundamentals in a given year and the regulatory value of the UFR valid in the prior year. We employ both the Nelson-Siegel and Svensson models to extrapolate yields over maturities of 21-30 years employing the selected value of the UFR and compare them with the observed yields using the mean square error statistic. Furthermore, we optimise the parameters of the proposed UFR formula by minimising the defined loss function capturing both mentioned factors.
Fulltext:  PDF
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Utilization of Radar Echo Extrapolation for Quantitative Precipitation Forecast
Frolík, Petr ; Novák, Petr (advisor) ; Žák, Michal (referee)
Title: Utilization of radar echo extrapolation for quantitative precipitation forecast Author: Petr Frolík Department: Department of Meteorology and Enviroment Protection Supervisor: RNDr. Petr Novák, PhD., ČHMÚ Supervisor's e-mail address: petr_novak@chmi.cz Abstract: At present time weather radar data are essential for national meteorological services. Utilization of this data for quantitative precipitation forecast and severe weather prediction for short period (nowcasting) becomes more and more common. Increasing interest for quantitative precipitation forecasts can be noticed in hydrological applications, where it can give early warning on flash floods and can improve large scale precipitation forecasts. This paper verifies usability of COTREC nowcasting method based on extrapolation of radar echo for quantitative precipitation forecast. Quality of COTREC forecast up to 3 hours was investigated on data from 1.4.2006 to 30.9.2006. Comparison of COTREC method with Aladin NWP model forecasts was also made. Hourly mean precipitation estimates on catchments were chosen for comparison because of verification focused mainly on utilization of the forecasts in hydrological applications. Forecasted precipitation estimates were compared with optimal operationally available precipitation estimate - adjusted radar...
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Quantitative Easing and its Impact on Wealth Inequality
Lazar, Stefan-Alexandru ; Taušer, Josef (advisor) ; Čajka, Radek (referee)
The aim of this thesis is to show how the unconventional monetary policy rounds of Quantitative Easing introduced in the United States between 2008 and 2014 have led to an increase in wealth inequality. The need for the thesis arises due to the uncharted nature of QE and because of more and more information is surfacing to light which points to this connection. By analysing the distribution of these funds and adding it to the then base distribution of money supply, this study was able to determine a significant 10 % increase in the Gini Index. Furthermore it highlights how a large portion of wealth was transferred from the middle class over to the top 5 % income households. Starting from a set of assumptions the calculation is performed by extrapolating the data required and by isolating the system from any external variables. The result is a theoretical model meant to describe the mechanism that links Quantitative Easing to wealth inequality. Moreover a detailed comparison is provided with the effect of a conventional monetary policy such as Open-Market Operations. Finally solutions to this issue are being discussed from economical, political and fiscal standpoints.
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Rain Prediction Using Meteo-Radar
Gerych, Petr ; Hradiš, Michal (referee) ; Szőke, Igor (advisor)
This paper deal with the rain prediction in the short time interval. The static pictures from meteo-radar serves as input data. The principle of meteo-radar is explained. The possible methods of the object detection and registration, motion interpolation and extrapolation is described. The flood fill algorithm and Lagrange extrapolation is applied to rain prediction. Application is written in C++ language under OS Linux. The example of the software application results is included.
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