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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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