|
|
On convergence of a series
Procházka, Antonín ; Zelený, Miroslav (advisor) ; Kaplický, Petr (referee)
in English This text is devoted to the series, whose n-th term is defined by (−1)n |sin n| /n. The goal of this work is to prove convergence of this series. The solution uses standard convergence tests, the theory of Fourier Series and findings about approximation of number π. 1
|
|
|
Development of laboratory exercises for subject the Signals and systems analysis
Doleček, Josef ; Mucha, Ján (referee) ; Zvončák, Vojtěch (advisor)
The bachelor thesis deals with basic operation with signals and, using demonstrative applications in Matlab, it should explain these operation to CASS (Signals and Systems Analysis) students. In the theory part continuous-time signals (signals classification, periodic signals, Fourier series), complex numbers, sampling and discrete-time signals (operation of convolution and correlation) are described. Practical applications explain: square signal harmonics synthesis, two discrete-time signals convolution and cross-correlation, object distance detection by radar using cross-correlation, complex model of harmonic signal and signals sampling.
|
|
|
Web-Based Demo of Fourier Transform for Signal Processing Courses
Hyrš, Martin ; Plchot, Oldřich (referee) ; Černocký, Jan (advisor)
The aim of this work is to create a program demonstrating the Fourier transform. The introductory section summarizes the theory of Fourier transform and shows the procedure for its numerical approximation. The following chapter describes the existing applets. Subsequently, the concept of the demonstration and its implementation are described. The final part contains tutorial examples of using the application and summary of users' reactions.
|
|
|
Semianalytical Computation of Fourier Series Coeficients
Hégr, Tomáš ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis deals with semianalytical computation of the coefficients of the Fourier series. The aim of this work is to create a graphical user interface for program TKSL/C. The work contains the theory of Fourier series and Fourier transforms. The state of the art software is described in the following chapter. In the next parts the thesis describes the concept of the implementation of the user interface, some tutorial examples which were used and the summary of user testing.
|
|
|
Semi-Analytical Computations
Herzallah, Ahmad Sudqi Hussein ; Kopřiva, Jan (referee) ; Kunovský, Jiří (advisor)
This thesis discusses the analytical errors emerging from semi-analytical calculations. It also discusses about the modern method of Taylor's series for numerical calculations of ordinary differential equations and chosen methods of charachterized functions. The end solutions indicate favourable results for the semi-analytical calculations in the selected roles and responsible differential equations by direct execution of Taylor's series for solutions of polynomial functions, exponential functions & geometric functions using simulation program "TKSL". It also discusses about the definite & indefinite Intergals and methods for the solution of definite integrals. Followed by a brief introduction of Maple, Matlab & TKSL and further comparison of the result of the three programs & finding the best way of resolving the definite integrals.
|
|
| |
|
|
Presentation of selected themes of BSIS in PPT-environment
Havlín, Radomil ; Šebesta, Vladimír (referee) ; Sigmund, Milan (advisor)
The bachelors thesis occupy by topics of the course BSIS, which can be presented by the multimedia and animation techniques in the presentation. In the introduction, these topics are given a different method of processing. In most cases, provides a modular solution by demonstration and argued spectrum signal. The chapters describe the operation with one, two signals at the time, the properties of Fourier transform with illustrative demonstration, the correlation with convolution, kvaziperiodické signals and the last chapter the spectrum of selective signals.
|
|
| |
|
|
The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
|
|
|
The Fourier Series and Its Properties
Sladká, Pavla ; Žák, Libor (referee) ; Štarha, Pavel (advisor)
The functional series, and especially the Fourier series, are an important mathematical apparatus exploited in the various technical branches. A very essential group of the functional series are the power series, which are applied because of their simplicity for solving of the many problems. An expansion of the function to the power series, i. e. the Taylor expansion, whose sum is the expanded function. These expansions are suitable for evaluation of operations, such as calculation of functional values, limits, derivatives and integrals. Calculations of these expansions are easier than of the functions theirself. The Fourier series are used for studies of events with periodic character. An advantage of the Fourier series is the fact, that the requirements for convergency are weaker than in case of the Taylor expansions. Likewise, calculation of the coefficients can be more simple than in the Taylor expansions. Expansions of functions to the Fourier series are used especially for solving ordinary and partial differential equations. This method of solving is known as the Fourier method or the Fourier method of variable separation.
|
guest ::
