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Reccurence plot for heart rate variability analysis
Franěk, Pavel ; Čmiel, Vratislav (referee) ; Janoušek, Oto (advisor)
The aim of this thesis is to describe the variability of cardiac rhythm and familiarity with the methods of the analysis, ie by monitoring changes in heart rhythm electrogram signal recording and using the methods in the time domain using recurrent diagram. The work describes the quantification of the methods and possibilities of quantifiers in the evaluation of heart rate variability analysis. It also describes the clinical significance of heart rate variability and diagnostic capabilities changes of heart rate variability caused by ischemic heart disease. The practical part describes how to create applications in Matlab to calculate the quantifiers analysis of heart rate variability in the time domain using recurrent diagram. The calculation was made of the positions R wave elektrogram signal isolated rabbit hearts. The calculated values of quantifiers both methods were statistically evaluated and discussed.
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Signal Decomposition using EMD transform
Mžourek, Zdeněk ; Mekyska, Jiří (referee) ; Smékal, Zdeněk (advisor)
Aim of this thesis is to introduce empiric mode decomposition as a method for decomposing arbitrarily nonlinear and non-stationary signal into intrinsic mode functions. Using empiric modal decomposition together with Hilbert transform produces instantaneous frequency. We can use this instatenous frequency to create a Hilbert spectrum and use it for analysis in time-frequency domain. In next part we show several drawbacks of this method. We also present several ways how to improve empirical mode decomposition algorithm to obtain better results. An example of decomposition by empiric mode decompositon is made to illustrate how the whole procedure works.
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Interpolace hladkých funkcí pomocí kvadratických a kubických splinů
Eckstein, Jiří ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
In this thesis, we study properties of cubic and quadratic spline interpolation. First, we define the notions of spline and interpolation. We then merge them to study cubic and quadratic spline interpolations. We go through the individual spline interpolation types, show an algorithm for constructing selected types and sum up their basic properties. We then present a computer program based on the provided algorithms. We use it to construct spline interpolations of some sample functions and we calculate errors of these interpolation and compare them with theoretical estimates.
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Smoothing quadratic and cubic splines
Oukropcová, Kateřina ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
Title: Smoothing quadratic and cubic splines Author: Kateřina Oukropcová Department: Department of Numerical Mathematics Supervisor: RNDr. Václav Kučera, Ph.D., Department of Numerical Mathematics Abstract: The aim of this bachelor thesis is to study the topic of smoothing quadratic and cubic splines on uniform partitions. First, we define the basic con- cepts in the field of splines, next we introduce interpolating splines with a focus on their minimizing properties for odd degree and quadratic splines and finally smoo- thing odd degree and quadratic splines. We derive algorithms for the construction of smoothing cubic and quadratic splines. In the last chapter, the presented al- gorithms are implemented in Matlab and applied to test data. Obtained results are presented in graphic form and discussed. Keywords: interpolation, approximation, cubic spline, quadratic spline, smoo- thing spline 1
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Interpolace hladkých funkcí pomocí kvadratických a kubických splinů
Eckstein, Jiří ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
In this thesis, we study properties of cubic and quadratic spline interpolation. First, we define the notions of spline and interpolation. We then merge them to study cubic and quadratic spline interpolations. We go through the individual spline interpolation types, show an algorithm for constructing selected types and sum up their basic properties. We then present a computer program based on the provided algorithms. We use it to construct spline interpolations of some sample functions and we calculate errors of these interpolation and compare them with theoretical estimates.
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Signal Decomposition using EMD transform
Mžourek, Zdeněk ; Mekyska, Jiří (referee) ; Smékal, Zdeněk (advisor)
Aim of this thesis is to introduce empiric mode decomposition as a method for decomposing arbitrarily nonlinear and non-stationary signal into intrinsic mode functions. Using empiric modal decomposition together with Hilbert transform produces instantaneous frequency. We can use this instatenous frequency to create a Hilbert spectrum and use it for analysis in time-frequency domain. In next part we show several drawbacks of this method. We also present several ways how to improve empirical mode decomposition algorithm to obtain better results. An example of decomposition by empiric mode decompositon is made to illustrate how the whole procedure works.
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Reccurence plot for heart rate variability analysis
Franěk, Pavel ; Čmiel, Vratislav (referee) ; Janoušek, Oto (advisor)
The aim of this thesis is to describe the variability of cardiac rhythm and familiarity with the methods of the analysis, ie by monitoring changes in heart rhythm electrogram signal recording and using the methods in the time domain using recurrent diagram. The work describes the quantification of the methods and possibilities of quantifiers in the evaluation of heart rate variability analysis. It also describes the clinical significance of heart rate variability and diagnostic capabilities changes of heart rate variability caused by ischemic heart disease. The practical part describes how to create applications in Matlab to calculate the quantifiers analysis of heart rate variability in the time domain using recurrent diagram. The calculation was made of the positions R wave elektrogram signal isolated rabbit hearts. The calculated values of quantifiers both methods were statistically evaluated and discussed.
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Analysis of methods for constructing yield curves
Matějka, Martin ; Janeček, Martin (advisor) ; Sitař, Milan (referee)
The thesis is focused on finding the most appropriate method for constructing the yield curve which will meet the criteria of Solvency II and also the selected evaluation criteria. An overview of advantages of each method is obtained by comparing these methods. Yield curves are constructed using the Czech interest rate swap data from 2007 to 2013. The selection of the evaluated methods respects their public availability and their practical application in life insurance or central banks. This thesis is divided into two parts. The first part describes the theoretical background which is necessary to understand the examined issues. In the second part the analysis of selected methods was carried out with detailed evaluation.
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