Fourier analysis on finite groups with applications in signal processing and system design / / Radomir S. Stankovic, Claudio Moraga, Jaakko Astola

• Record Nr.: UNINA9911018808903321
• Autore: Stankovic Radomir S
• Pubbl/distr/stampa: Piscataway, NJ, : IEEE Press; Hoboken, N.J., : Wiley-Interscience, c2005
• ISBN: 9786610277933; 9781280277931; 1280277939; 9780471745433; 047174543X; 9781601193766; 1601193769; 9780471745426; 0471745421
• Descrizione fisica: 1 online resource (262 p.)
• Altri autori (Persone): MoragaClaudio; AstolaJaakko
• Disciplina: 621.382/2
• Soggetti: Signal processing - Mathematics; Fourier analysis; Non-Abelian groups
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Preface -- Acknowledgments -- Acronyms -- 1 Signals and Their Mathematical Models -- 1.1 Systems -- 1.2 Signals -- 1.3 Mathematical Models of Signals -- References -- 2 Fourier Analysis -- 2.1 Representations of Groups -- 2.1.1 Complete Reducibility -- 2.2 Fourier Transform on Finite Groups -- 2.3 Properties of the Fourier Transform -- 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups -- 2.5 Fast Fourier Transform on Finite Non-Abelian Groups -- References -- 3 Matrix Interpretation of the FFT -- 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups ; -- 3.2 Illustrative Examples -- 3.3 Complexity of the FFT -- 3.3.1 Complexity of Calculations of the FFT -- 3.3.2 Remarks on Programming Implememtation of FFT -- 3.4 FFT Through Decision Diagrams -- 3.4.1 Decision Diagrams -- 3.4.2 FFT on Finite Non-Abelian Groups Through DDs -- 3.4.3 MMTDs for the Fourier Spectrum -- 3.4.4 Complexity of DDs Calculation Methods -- References -- 4 Optimization of Decision Diagrams -- 4.1 Reduction Possibilities in Decision Diagrams -- 4.2 Group-Theoretic Interpretation of DD -- 4.3 Fourier Decision Diagrams -- 4.3.1 Fourier Decision Trees -- 4.3.2 Fourier Decision Diagrams -- 4.4 Discussion of Different Decompositions -- 4.4.1 Algorithm for Optimization of DDs -- 4.5 Representation of Two-Variable Function Generator -- 4.6 Representation of Adders by Fourier DD -- 4.7 Representation of Multipliers by Fourier DD -- 4.8 Complexity of NADD -- 4.9 Fourier DDs with Preprocessing -- 4.9.1 Matrix-valued Functions -- 4.9.2 Fourier Transform for Matrix-Valued Functions -- 4.10 Fourier Decision Trees with Preprocessing -- 4.11 Fourier Decision Diagrams with Preprocessing -- 4.12 Construction of FNAPDD -- 4.13 Algorithm for Construction of FNAPDD -- 4.13.1 Algorithm for Representation -- 4.14 Optimization of FNAPDD -- References -- 5 Functional Expressions on Quaternion Groups -- 5.1 Fourier Expressions on Finite Dyadic Groups -- 5.1.1 Finite Dyadic Groups -- 5.2 Fourier Expressions on Q2.; 5.3 Arithmetic Expressions -- 5.4 Arithmetic Expressions from Walsh Expansions -- 5.5 Arithmetic Expressions on Q2 -- 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions -- 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions -- 5.6 Different Polarity Polynomials Expressions -- 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2) -- 5.6.2 Fixed-Polarity Arithmetic-Haar<U+0083>Expressions -- 5.7 Calculation of the Arithmetic-Haar Coefficients -- 5.7.1 FFT-like Algorithm -- 5.7.2 Calculation of Arithmetic-Haar Coefficients Through Decision Diagrams -- References -- 6 Gibbs Derivatives on Finite Groups -- 6.1 Definition and Properties of Gibbs Derivatives on Finite Non-Abelian Groups -- 6.2 Gibbs Anti-Derivative -- 6.3 Partial Gibbs Derivatives -- 6.4 Gibbs Differential Equations -- 6.5 Matrix Interpretation of Gibbs Derivatives -- 6.6 Fast Algorithms for Calculation of Gibbs Derivatives on Finite Groups -- 6.6.1 Complexity of Calculation of Gibbs Derivatives -- 6.7 Calculation of Gibbs Derivatives Through DDs -- 6.7.1 Calculation of Partial Gibbs Derivatives.<U+0083> -- References -- 7 Linear Systems on Finite Non-Abelian Groups -- 7.1 Linear Shift-Invariant Systems on Groups -- 7.2 Linear Shift-Invariant Systems on Finite Non-Abelian Groups -- 7.3 Gibbs Derivatives and Linear Systems -- 7.3.1 Discussion -- References -- 8 Hilbert Transform on Finite Groups -- 8.1 Some Results of Fourier Analysis on Finite Non-Abelian Groups -- 8.2 Hilbert Transform on Finite Non-Abelian Groups -- 8.3 Hilbert Transform in Finite Fields -- References -- Index.
• Sommario/riassunto: Discover applications of Fourier analysis on finite non-Abelian groups The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods. Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design examines aspects of Fourier analysis on finite non-Abelian groups and discusses different methods used to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as an example of discrete functions in engineering practice. Additionally, consideration is given to the polynomial expressions and ; decision diagrams defined in terms of Fourier transform on finite non-Abelian groups. A solid foundation of this complex topic is provided by beginning with a review of signals and their mathematical models and Fourier analysis. Next, the book examines recent achievements and discoveries in: . Matrix interpretation of the fast Fourier transform. Optimization of decision diagrams. Functional expressions on quaternion groups. Gibbs derivatives on finite groups. Linear systems on finite non-Abelian groups. Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups in compact representations of discrete functions and related tasks in signal processing and system design, including logic design. All chapters are self-contained, each with a list of references to facilitate the development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this is an excellent textbook for graduate-level students and researchers in signal processing, logic design, and system theory-as well as the more general topics of computer science and applied mathematics.

Vacuum gas carburizing - fate of hydrocarbons

• Record Nr.: UNINA9910346931403321
• Autore: Khan Rafi Ullah
• Pubbl/distr/stampa: KIT Scientific Publishing, 2008
• ISBN: 1000009231
• Descrizione fisica: 1 online resource (II, 159 p. p.)
• Soggetti: Biotechnology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Sommario/riassunto: This work focuses on gaseous reactive flows in ideal and non-ideal reactors. The objective of this research is the development of models for the numerical simulation of homogeneous reactive flows under ; vacuum carburizing conditions of steel with propane and acetylene. These models can be used for further investigations of heterogeneous reactions during vacuum carburizing of steel to predict the carbon flux on the complex shaped steel parts to understand and, eventually, optimize the behavior of the whole reactor.arburizing is the case-hardening process in which carbon is added to the surface of low-carbon steels at temperatures generally between 850 and 1050 °C. In the conventional gas carburizing at atmospheric pressure, the carbon potential is controlled by adjusting the flow rate of the carburizing gas. Carbon potential of the furnace atmosphere can be related to partial pressure of CO2 or O2 or vapour pressure of water by equilibrium relationships and a sensor can be used to measure it. This method of carbon-potential control cannot be used for vacuum gas carburizing due to the absence of thermodynamic equilibrium which is one of the main difficulties of the vacuum carburizing process. The formation of soot during carburization isalso undesirable and the process parameters should be selected such that the formation of soot is minimized. The amount of carbon available for carburizing the steel depends on the partial pressure of the carburizing gas, carbon content in the carburizing gas and the pyrolysis reactions of the carburizing gas. The pyrolysis reactions of the carburizing gas are also affected by the contacting pattern or how the gas flows through and contacts with the steel parts being carburized. This work focuses on gaseous reactive flows in ideal and non-ideal reactors. The objective of this research is the development of models for the numerical simulation of homogeneous reactive flows under vacuum carburizing conditions of steel with ropane and acetylene. These models can be used for further investigations of heterogeneous reactions during vacuum carburizing of steel to predict the carbon flux on the complex shaped steel parts to understand and, eventually, optimize the behavior of the whole reactor. Two different approaches have been used to model the pyrolysis of propane and acetylene under vacuum carburizing conditions of steel. One approach is based on formal or global kinetic mechanisms together with the computational fluid dynamics (CFD) tool. The other approach is based on detailed chemistry with simplified or ideal flow models. Two global mechanisms developed at the Engler-Bunte-Institut for pyrolysis of propane and acetylene respectively were used in this work. One detailed mechanism developed at the Institute of Chemical Technology by the research group of Professor Deutschmann was used for modeling the pyrolysis of both the propane and acetylene. Experimental data from investigations on vacuum carburizing conducted at the Engler-Bunte-Institut were used to validate the modeling results.