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SSI Dividing Numerical Integrator
Suntcov, Roman ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The thesis deals with numerical integration and hardware division operations. The reader is familiar with the numerical solution of differential equations through several different methods, for example Taylor's series. Furthermore, it is discussed the operation of division in the hardware and the method of its implementation in the FPGA. Subsequently, a parallel-parallel and serial-parallel integrator is designed. The practical aim of the thesis is to design and implement a serial-serial dividing integrator and create a simulator for it.
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Division Operation Simulation
Matečný, František ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with numerical integration and division operation. The reader is acquainted with the numerical solution of differential equations using division by the Taylor series. Next is explained the principle of SRT division in hardware and introduction of draft of design series-parallel and parallel division integrator in fixed point arithmetic. The practical aim of this work is implementation parallel division integrator and development of a software simulation of this integrator.
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Audio equalizer implementation based on FPGA structure
Otisk, Libor ; Valach, Soběslav (referee) ; Kváš, Marek (advisor)
The bachelor thesis introduces the basic types of audio equalizers. It describes the design of digital filters for graphic equalizer, the correct choice of structure, placement and shape of digital filters. It also describes the implementation of graphic equalizer in the fixed-point arithmetic. It further describes an implementation of the algorithm graphic equalizer on PC and the implementation in gate array of FPGA.
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Simulation tool for fixed-point arithmetic
Grézl, Vojtěch ; Kunz, Jan (referee) ; Čala, Martin (advisor)
This bachelor's thesis is focused on creating tool for simulating calculations with fixed point. This tool simplifies and increases the efficiency of performing operations with values of different data types. By calculating and graphically displaying absolute errors, which creates a conversion of values between data types and conversion through maximum absolute errors, the user can evaluate whether this conversion is optimal or not. After getting acquainted with this issue in the theoretical introduction part, the design of the practical part follows, which summarizes the implementation and procedure of program design in the LabVIEW 2021. Process of draft of the practical part is based on attributes of LabVIEW and it’s part FPGA module and aim on creating of transparent and user-friendly user interface. The output of the practical part is a tool that works with the created VI, containing a sequence of different operations with different input and output data types. The program is used to convert numbers of different data types to another type, mainly for a conversion to a fixed point data type. The user gives the main direction by creating a sample VI, the operations of which will then be performed. Other parameters that the user can set and affect the program are listed on the user interface.
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Abstraction in Automata Algorithms
Kocourek, Tomáš ; Lengál, Ondřej (referee) ; Holík, Lukáš (advisor)
Tato práce si klade za cíl implementaci a experimentální porovnání protiřetězcových algoritmů s abstrakcí a bez abstrakce, které testují prázdnost alternujících automatů. Autor také navrhuje vlastní algoritmy s abstrakcí a navrhuje několik optimalizací pro existující abstraktní algoritmy. Práce popisuje teoretické pozadí studovaných algoritmů a navrhuje efektivní způsob implementace datových struktur, které jsou těmito algoritmy používány. Experimentální vyhodnocení na náhodných automatech ukazuje, že algoritmy bez abstrakce vykazují obecně lepší výsledky, neboť nevyužívají náročné operace průniku a komplementace shora a zdola uzavřených množin. V případě automatů s vysokou hustotou přechodů však algoritmy bez abstrakce zpomalují a algoritmy s abstrakcí naopak zrychlují.
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Implementation of fixed-point arithmetic unit in FPGA
Kalocsányi, Vít ; Fujcik, Lukáš (referee) ; Dvořák, Vojtěch (advisor)
This thesis deals with a design of fixed-point arithmetic unit for FPGA circuits and its model in Matlab. The thesis explains a number representation in digital circuits and both basic and selected additional arithmetic operations with fixed-point numbers. The arithmetic unit’s model is designed in Matlab, the realization of the unit in VHDL is described and its implementation into FPGA is carried out. A specific example of use of designed arithmetic unit’s model for simulation of complex systems in Simulink environment is shown at the end of the thesis.
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Simulation tool for fixed-point arithmetic
Grézl, Vojtěch ; Kunz, Jan (referee) ; Čala, Martin (advisor)
This bachelor's thesis is focused on creating tool for simulating calculations with fixed point. This tool simplifies and increases the efficiency of performing operations with values of different data types. By calculating and graphically displaying absolute errors, which creates a conversion of values between data types and conversion through maximum absolute errors, the user can evaluate whether this conversion is optimal or not. After getting acquainted with this issue in the theoretical introduction part, the design of the practical part follows, which summarizes the implementation and procedure of program design in the LabVIEW 2021. Process of draft of the practical part is based on attributes of LabVIEW and it’s part FPGA module and aim on creating of transparent and user-friendly user interface. The output of the practical part is a tool that works with the created VI, containing a sequence of different operations with different input and output data types. The program is used to convert numbers of different data types to another type, mainly for a conversion to a fixed point data type. The user gives the main direction by creating a sample VI, the operations of which will then be performed. Other parameters that the user can set and affect the program are listed on the user interface.
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Algorithm for word morphisms fixed points
Matocha, Vojtěch ; Holub, Štěpán (advisor) ; Žemlička, Jan (referee)
In the present work we study the first polynomial algorithm, which tests if the given word is a fixed point of a nontrivial morphism. This work contains an improved worst-case complexity estimate O(m · n) where n denotes the word length and m denotes the size of the alphabet. In the second part of this work we study the union-find problem, which is the crucial part of the described algorithm, and the Ackermann function, which is closely linked to the union-find complexity. We summarize several common methods and their time complexity proofs. We also present a solution for a special case of the union-find problem which appears in the studied algorithm. The rest of the work focuses on a Java implementation, whose time tests correspond to improved upper bound, and a visualization useful for particular entries.
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Arithmetical completeness of the logic R
Holík, Lukáš ; Švejdar, Vítězslav (advisor) ; Bílková, Marta (referee)
The aim of this work is to use contemporary notation to build theory of Rosser logic, explain in detail its relation to Peano arithmetic, show its Kripke semantics and finally using plural self-reference show the proof of arithmetical completeness. In the last chapter we show some of the properties of Rosser sentences. Powered by TCPDF (www.tcpdf.org)
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Commuting continuous functions without a common fixed point
Karasová, Klára ; Vejnar, Benjamin (advisor) ; Cúth, Marek (referee)
The topic of the thesis are common fixed points of commuting functions. With the help of the Mountain climbing theorem we will prove the theorem about extending commuting functions, which will allow us to construct commuting self-mappings of the unit interval with no common fixed point. For the next part we prove several versions of the extending commuting functions theorem using different versions of the Mountain climbing theorem. We will also prove that if X is a dendroid, S an abelian semigroup of continuous monotone self-mappings of X and f : X → X commutes with each element of S, then f and S have a common fixed point. 1
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