Tag Archives: first-order

Study and Design of Differential Microphone Arrays

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Jacob Benesty, Jingdong Chen, "Study and Design of Differential Microphone Arrays"
English | 2013 | ISBN-10: 364233752X, 3642427561 | 180 pages | PDF | 6 MB

Study and Design of Differential Microphone Arrays
Microphone arrays have attracted a lot of interest over the last few decades since they have the potential to solve many important problems such as noise reduction/speech enhancement, source separation, dereverberation, spatial sound recording, and source localization/tracking, to name a few. However, the design and implementation of microphone arrays with beamforming algorithms is not a trivial task when it comes to processing broadband signals such as speech. Indeed, in most sensor arrangements, the beamformer output tends to have a frequency-dependent response. One exception, perhaps, is the family of differential microphone arrays (DMAs) who have the promise to form frequency-independent responses. Moreover, they have the potential to attain high directional gains with small and compact apertures. As a result, this type of microphone arrays has drawn much research and development attention recently. This book is intended to provide a systematic study of DMAs from a signal processing perspective. The primary objective is to develop a rigorous but yet simple theory

for the design, implementation, and performance analysis of DMAs. The theory includes some signal processing techniques for the design of commonly used first-order, second-order, third-order, and also the general Nth-order DMAs. For each order, particular examples are given on how to form standard directional patterns such as the dipole, cardioid, supercardioid, hypercardioid, subcardioid, and quadrupole. The study demonstrates the performance of the different order DMAs in terms of beampattern, directivity factor, white noise gain, and gain for point sources. The inherent relationship between differential processing and adaptive beamforming is discussed, which provides a better understanding of DMAs and why they can achieve high directional gain. Finally, we show how to design DMAs that can be robust against white noise amplification.
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Mathematics for Economics and Finance: Methods and Modelling

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Martin Anthony, Norman Biggs, "Mathematics for Economics and Finance: Methods and Modelling"
1996 | ISBN-10: 0521551137, 0521559138 | 410 pages | PDF | 12 MB

Mathematics for Economics and Finance: Methods and Modelling
Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.
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Mathematics for Economics and Finance: Methods and Modelling

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Martin Anthony, Norman Biggs, "Mathematics for Economics and Finance: Methods and Modelling"
1996 | ISBN-10: 0521551137, 0521559138 | 410 pages | PDF | 12 MB

Mathematics for Economics and Finance: Methods and Modelling
Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.
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A Formalization of Set Theory without Variables

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Alfred Tarski, Steven Givant, "A Formalization of Set Theory without Variables"
1987 | ISBN: 0821810413 | 318 pages | PDF | 29 MB

A Formalization of Set Theory without Variables
Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to computer scientists interested in developing very simple computer languages rich enough for mathematical and scientific applications. The authors show that set theory and number theory can be developed within the framework of a new, different, and simple equational formalism, closely related to the formalism of the theory of relation algebras. There are no variables, quantifiers, or sentential connectives. Predicates are constructed from two atomic binary predicates (which denote the relations of identity and set-theoretic membership) by repeated applications of four operators that are analogues of the well-known operations of relative product, conversion, Boolean addition, and complementation. All mathematical statements are expressed as equations between predicates. There are ten logical axiom schemata and just one rule of inference: the one of replacing equals by equals, familiar from high school algebra. Though such a simple formalism may appear limited in its powers of expression and proof, this book proves quite the opposite. The authors show that it provides a framework for the formalization of practically all known systems of set theory, and hence for the development of all classical mathematics. The book contains numerous applications of the main results to diverse areas of foundational research: propositional logic; semantics; first-order logics with finitely many variables; definability and axiomatizability questions in set theory, Peano arithmetic, and real number theory; representation and decision problems in the theory of relation algebras; and decision problems in equational logic.
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Mathematical Logic: Undergraduate Texts in Mathematics by H.D. Ebbinghaus

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Mathematical Logic: Undergraduate Texts in Mathematics by H.D. Ebbinghaus
English | Feby 1984 | ISBN: 0387908951 | 221 Pages | PDF | 6 MB
This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified?

Mathematical Logic: Undergraduate Texts in Mathematics by H.D. Ebbinghaus
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Mathematical Logic: Undergraduate Texts in Mathematics by H.D. Ebbinghaus

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Mathematical Logic: Undergraduate Texts in Mathematics by H.D. Ebbinghaus
English | Feby 1984 | ISBN: 0387908951 | 221 Pages | PDF | 6 MB
This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified?

Mathematical Logic: Undergraduate Texts in Mathematics by H.D. Ebbinghaus
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Mathematics of Modality

Robert Goldblatt, "Mathematics of Modality"
English | ISBN: 1881526240 | edition 1993 | PDF | 288 pages | 11,2 mb
Modal logic is the study of modalities – expressions that qualify assertions about the truth of statements. This volume collects together a number of the author's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic modals, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic.

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