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Transforms are an important part of an engineer’s toolkit for solving signal processing and polynomial computation problems. In contrast to the Fourier transform-based approaches where a fixed window is used uniformly for a range of frequencies, the wavelet transform uses short windows at high frequencies and long windows at low frequencies. This way, the characteristics of non-stationary disturbances can be more closely monitored. In other words, both time and frequency information can be obtained by wavelet transform. Instead of transforming a pure time description into a pure frequency description, the wavelet transform finds a good promise in a time-frequency description. Due to its inherent time-scale locality characteristics, the discrete wavelet transform (DWT) has received considerable attention in digital signal processing (speech and image processing), communication, computer science and mathematics. Wavelet transforms are known to have excellent energy compaction characteristics and are able to provide perfect reconstruction. Therefore, they are ideal for signal/image processing. The shifting (or translation) and scaling (or dilation) are unique to wavelets. Orthogonality of wavelets with respect to dilations leads to multigrid representation. The nature of wavelet computation forces us to carefully examine the implementation methodologies. As the computation of DWT involves filtering, an efficient filtering process is essential in DWT hardware implementation. In the multistage DWT, coefficients are calculated recursively, and in addition to the wavelet decomposition stage, extra space is required to store the intermediate coefficients. Hence, the overall performance depends significantly on the precision of the intermediate DWT coefficients. This work presents new implementation techniques of DWT, that are efficient in terms of computation requirement, storage requirement, and with better signal-to-noise ratio in the reconstructed signal.

Complex analysis --- Computer science --- Computer architecture. Operating systems --- Computer. Automation --- computervisie --- beeldverwerking --- complexe analyse (wiskunde) --- bedrijfssoftware --- computers --- computerkunde --- signaalverwerking

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The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.

Mathematical logic --- Complex analysis --- Mathematics --- Computer science --- Computer architecture. Operating systems --- complexe analyse (wiskunde) --- bedrijfssoftware --- wiskunde --- algoritmen --- logica

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This book constitutes the thoroughly refereed conference proceedings of the 9th International Symposium on Reconfigurable Computing: Architectures, Tools and Applications, ARC 2013, held in Los Angeles, CA, USA, in March 2013. The 28 revised papers presented, consisting of 20 full papers and 11 poster papers were carefully selected from 41 submissions. The topics covered are applications, arithmetic, design optimization for FPGAs, architectures, place and routing.

Complex analysis --- Computer science --- Computer architecture. Operating systems --- complexe analyse (wiskunde) --- bedrijfssoftware --- computers --- computerbesturingssystemen --- hardware --- OS (operating system) --- computernetwerken --- computerkunde

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An understanding of discrete mathematics is essential for students of computer science wishing to improve their programming competence. Fundamentals of Discrete Math for Computer Science provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions. Topics and features: Highly accessible and easy to read, introducing concepts in discrete mathematics without requiring a university-level background in mathematics Ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations Describes mathematical processes in an algorithmic manner, often including a walk-through demonstrating how the algorithm performs the desired task as expected Contains examples and exercises throughout the text, and highlights the most important concepts in each section Selects examples that demonstrate a practical use for the concept in question This easy-to-understand and fun-to-read textbook is ideal for an introductory discrete mathematics course for computer science students at the beginning of their studies. The book assumes no prior mathematical knowledge, and discusses concepts in programming as needed, allowing it to be used in a mathematics course taken concurrently with a student’s first programming course.

Complex analysis --- Discrete mathematics --- Computer science --- Computer architecture. Operating systems --- Computer. Automation --- complexiteit --- discrete wiskunde --- complexe analyse (wiskunde) --- bedrijfssoftware --- computers --- informatica --- computerkunde

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This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Mathematics --- Complex analysis --- Mathematical analysis --- Operational research. Game theory --- Discrete mathematics --- Computer architecture. Operating systems --- reeksen (wiskunde) --- discrete wiskunde --- complexe analyse (wiskunde) --- bedrijfssoftware --- speltheorie --- wiskunde