Algorithms for Discrete Fourier Transform and Convolution
|
|
- Magdalene Dixon
- 5 years ago
- Views:
Transcription
1 Algorithms for Discrete Fourier Transform and Convolution Second Edition Springer Science+Business Media, LLC
2 Signal Processing and Digital Filtering Synthetic Aperture Radar J.P. Fitch Multiplicative Complexity, Convolution and the DFf M.T. Heideman Array Signal Processing S.U. Pillai Maximum Likelihood Deconvolution J.M. Mendel Algorithms for Discrete Fourier Transform and Convolution Second Edition T. Tolimieri, M. An, and C. Lu Algebraic Methods for Signal Processing and Communications Coding R.E. Blahut Electromagnetic Devices for Motion Control and Signal Processing Y.M. Pulyer Mathematics of Multidimensional Fourier Transform Algorithms Second Edition R. Tolimieri, M. An, and C. Lu Lectures on Discrete Time Filtering R.S. Bucy Distributed Detection and Data Fusion P.K. Varshney
3 Richard Tolimieri Myoung An Chao Lu Algorithms for Discrete Fourier Transform and Convolution Second Edition C.S. Burrus Consulting Editior Springer
4 Richard Tolimieri Department of Electrical Engineering City College of CUNY New York, NY 10037, USA MyoungAn A.J. Devaney Associates 52 Ashford Street Allston, MA 02134, USA Chao Lu Department of Computer and Information Sciences Towson State University Towson, MD 21204, USA Consulting Editor Signal Processing and Digital Filtering C.S. Burrus Professor and Chairman Department of Electrical and Computer Engineering Rice University Houston, TX , USA Library of Congress Cataloging-in-Publication Data Tolimieri, Richard, Algorithms for discrete Fourier transform and convolution / Richard Tolimieri, Myoung An, Chao Lu. p. cm. - (Signal processing and digital filtering) Includes bibliographical references (p. ) and index. ISBN (alk. paper) I. Fourier transformations- Data processing. 2. Convolutions (Mathematics)- Data processing. 3. Digital filters (Mathematics) I. An, Myoung. 11. Lu, Chao Title. IV. Series. QA403.5.T '.723-dc Printed on acid-free paper Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc. in 1997 Softcover reprint of the hardcover 2nd edition 1997 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely byanyone. Production managed by Anthony Battle; manufacturing supervised by Johanna Tschebull. Photocomposed pages prepared from the authors' ~1EJX files ISBN ISBN (ebook) DOI /
5 Preface This book is based on several courses taught during the years at the City College of the City University of New York and at Fudan University, Shanghai, China, in the summer of It was originally our intention to present to a mixed audience of electrical engineers, mathematicians and computer scientists at the graduate level a collection of algorithms that would serve to represent the vast array of algorithms designed over the last twenty years for computing the finite Fourier transform (FFT) and finite convolution. However, it was soon apparent that the scope of the course had to be greatly expanded. For researchers interested in the design of new algorithms, a deeper understanding of the basic mathematical concepts underlying algorithm design was essential. At the same time, a large gap remained between the statement of an algorithm and the implementation of the algorithm. The main goal of this text is to describe tools that can serve both of these needs. In fact, it is our belief that certain mathematical ideas provide a natural language and culture for understanding, unifying and implementing a wide range of digital signal processing (DSP) algorithms. This belief is reinforced by the complex and time-consuming effort required to write code for recently available parallel and vector machines. A significant part of this text is devoted to establishing rules and procedures that reduce and at times automate this task. In chapter 1, a survey is given of basic algebra. It is assumed that much of this material is not newj in any case, the facts are easily described. The tensor product is introduced in chapter 2. The importance of the tensor product will be a reoccurring theme throughout this text. Tensor product factors have a direct interpretation as machine instructions on many vector
6 vi Preface and parallel computers. Tensor product identities provide linguistic rules for manipulating algorithms to match specific machine characteristics. Inherent in these rules are certain permutations, called stride permutations, which can be impiemented on many machines by a single instruction. The tedious effort of readdressing, required in many DSP algorithms, is greatly reduced. Also, the data ßow is highlighted, which is especially important on supercomputers where the data ßow is usually the major factor that determines the efficiency of the computation. The design of fast FFT algorithms can be dated back historically to the times of Gauss (1805) [1]. The collected work of some unpublished manuscripts by Gauss contained the essentials of the Cooley-Tukey FFT algorithm, but it did not attract much attention. In 1965, when Cooley and Tukey published their paper [2], known as the fast Fourier transform algorithm, the computing science started a revolutionary era. Since then, many variants of the Cooley-Tukey FFT algorithm have been developed. In chapters 3 and 4 of this book, the Cooley-Tukey FFT algorithm, along with its many variants, are unified under the banner of tensor product. From one point of view, these algorithms depend on mapping a one-dimensional array of data onto a multidimensional array of data (depending on the degree of compositeness of the transform size). Using tensor product we need to derive only the simplest case of mapping into a two-dimensional array. Tensor product identities can then be used to derive the general case. An explicit description of the data ßow is automatically given along with rules for varying this data ßow, if necessary. In chapter 5, the Good-Thomas prime factor algorithm is reformulated by tensor product. In chapters 6 and 7, various linear and cyclic convolution algorithms are described. The Chinese Remainder Theorem (CRT) for polynomials is the major tool. Matrix and tensor product formulations are used wherever possible. Results of Cook and Toom and Winograd are emphasized. The integer CRT is applied in chapter 7 to build a large convolution algorithm from efficient small convolution algorithms (Agarwal-Cooley). The scene changes in chapter 8. Various multiplicative FFT algorithms (depending on the ring structure of the indexing set) are described. The prime size algorithms are due to Rader. Winograd generalized Rader's method to composite transform size. We emphasize a variant of the Rader Winograd method. Tensor product language is used throughout, and tensor product identities serve as powerful tools for obtaining several variants that offer arithmetic and data ßow options. In chapter 13, we consider the duality between periodic and decimated data established by the Fourier transform. This duality is applied in the computation of the Fourier transform of odd prime power transform sizes, say pk. The ring structure of the indexing set has an especially simple ideal structure (local ring). The main result decomposes the computation of the Fourier transform into two pieces. The first is a Fourier transform of transform size pk-2. The description of the second is the main objective
7 Preface vii of chapters 14 and 15, where we introduce the theory of multiplicative characters and derive formulas for computing the Fourier transform of multiplicative characters. The authors are indebted to the patience and knowledge of L. Auslander, J. Cooley and S. Winograd, who, Over the years at IBM, Yorktown Heights, and at the City University of New York, have taken time to explain their works and ideas. The authors wish to thank C. S. Burrus, who read the manuscript of the book and suggested many improvements. We wish to thank DARPA for its support during the formative years of writing this book, and AFOSR for its support during the last two years, in which time the ideas of this book have been tested and refined in applications to electromagnetics, multispectral imaging, and imaging through turbulance. Whatever improvements in this revision are due to the routines written in these applications. Richard Tolimieri Myoung An Chao Lu
8 Contents Preface v 1 Review of Applied Algebra Introduction The Ring of Integers The Ring ZjN Chinese Remainder Theorem (CRT) Unit Groups Polynomial Rings Field Extension The Ring F[xl/ f(x) CRT for Polynomial Rings References Problems Tensor Product and Stride Permutation Introduction Tensor Product Stride Permutations Multidimensional Tensor Products Vector Implementation Parallel Implementation References Problems
9 x Contents 3 Cooley-Tukey FFT Algorithms 3.1 Introduction 3.2 Basic Properties of FT Matrix 3.3 An Example of an FT Algorithm 3.4 Cooley-Tukey FFT for N = 2M 3.5 Twiddle Factors 3.6 FT Factors. 3.7 Variants of the Cooley-Thkey FFT 3.8 Cooley-Thkey FFT for N = M L. 3.9 Arithmetic Cost References. Problems 4 Variants of FT AJgorithms and Implementations 4.1 Introduction 4.2 Radix-2 Cooley-Thkey FFT Algorithm 4.3 Pease FFT Algorithm 4.4 Auto-Sorting FT Algorithm 4.5 Mixed Radix Cooley-Tukey FFT. 4.6 Mixed Radix Agarwal-Cooley FFT 4.7 Mixed Radix Auto-Sorting FFT 4.8 Summary References Problems 5 Good-Thomas PFA 5.1 Introduction 5.2 Indexing by the CRT 5.3 An Example, N = Good-Thomas PFA for the General Case 5.5 Self-Sorting PFA References Problems 6 Linear and Cyclic Convolutions 6.1 Definitions Convolution Theorem Cook-Toom Algorithm Winograd Small Convolution Algorithm Linear and CycHc Convolutions Digital Filters References Problems
10 Contents xi 7 Agarwal-Cooley Convolution Algorithm Two-Dimensional Cyclic Convolution Agarwal-Cooley Algorithm References Problems Multiplicative Fourier Transform Algorithm References MFTA: The Prime Case 9.1 The Field Z/p The Fundamental Factorization Rader's Algorithm Reducing Additions Winograd Small FT Algorithm Summary... References.... Problems MFTA: Product of Two Distinct Primes 10.1 Basic Algebra Transform Size: Fundamental Factorization: Variants: Transform Size: pq Fundamental Factorization: pq Variants Summary References.... Problems MFTA: Composite Size 11.1 Introduction Main Theorem Product of Three Distinct Primes Variants Transform Size: Transform Size: 4p, p odd prime Transform Size: References Problems. 12 MFTA: r? 12.1 Introduction 12.2 An Example:
11 xii Contents 12.3 The General Case: r? 12.4 An Example: 33.. References. Problems Periodization and Decimation 13.1 Introduction Periodic and Decimated Data FT of Periodic and Decimated Data The Ring Z/pm... Problems Multiplicative Characters and the FT 14.1 Introduction Periodicity Periodic Multiplicative Characters Periodization and Decimation 14.3 F(P) of Multiplicative Characters F(pm) of Multiplicative Characters Primitive Multiplicative Characters Nonprimitive Multiplicative Characters Orthogonal Basis Diagonalizing F(P) Orthogonal Basis Diagonalizing F(pm) Orthogonal Basis of W Orthogonal Diagonalizing Basis References. Problems Rationality 15.1 An Example: Prime Case An Example: Transform Size: p Exponential Basis 15.6 Polynomial Product Modulo a Polynomial 15.7 An Example: 33 References.... Index
Yves Nievergelt. Wavelets Made Easy. Springer Science+Business Media, LLC
Wavelets Made Easy Yves Nievergelt Wavelets Made Easy Springer Science+Business Media, LLC Yves Nievergelt Department of Mathematics Eastem Washington University Cheney, WA 99004-2431 USA Library of Congress
More informationITSM: An Interactive Time Series Modelling Package for the pe
ITSM: An Interactive Time Series Modelling Package for the pe Peter J. Brockwell Richard A. Davis ITSM: An Interactive Time Series Modelling Package for the pe With 53 Illustrations and 3 Diskettes Written
More informationComputer-Aided Design in Magnetics
Computer-Aided Design in Magnetics D. A. Lowther P. P. Silvester Computer-Aided Design in Magnetics With 84 illustrations Springer-Verlag Berlin Heidelberg New York Tokyo D. A. Lowther Associate Professor
More informationUsing MSC/NASTRAN: Statics and Dynamics
Using MSC/NASTRAN: Statics and Dynamics A.D. Cifuentes Using MSC/NASTRAN Statics and Dynamics With 94 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Arturo O. Cifuentes
More informationThe MATLAB 5 Handbook
The MATLAB 5 Handbook Springer New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Singapore Tokyo Darren Redfern Colin Campbell The MATLAB 5 Handbook Springer Darren Redfern Practical
More informationVisualization in Supercomputing
Visualization in Supercomputing Raul H. Mendez Editor Visualization in Supercomputing With 166 Illustrations, 25 in Color Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Raul H.
More informationComputer Networks and Systems
Computer Networks and Systems Queueing Theory and Performance Evaluation Third Edition Springer Science+Business Media, LLC Thomas G. Robertazzi Computer Networks and Systems Queueing Theory and Performance
More informationProgramming with Turing and Object Oriented Turing
Programming with Turing and Object Oriented Turing Peter Grogono Programming with Turing and Object Oriented Turing Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest
More informationINVERSE PROBLEMS IN GROUNDWATER MODELING
INVERSE PROBLEMS IN GROUNDWATER MODELING Theory and Applications of Transport in Porous Media Series Editor: Jacob Bear, Technion - Israel Institute of Technology, Haifa, Israel Volume 6 The titles published
More informationModeling and Simulation in Scilab/Scicos with ScicosLab 4.4
Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4 Stephen L. Campbell, Jean-Philippe Chancelier and Ramine Nikoukhah Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4 Second Edition
More informationGuide to RISC Processors
Guide to RISC Processors Sivarama P. Dandamudi Guide to RISC Processors for Programmers and Engineers Sivarama P. Dandamudi School of Computer Science Carleton University Ottawa, ON K1S 5B6 Canada sivarama@scs.carleton.ca
More informationHIGH SPEED REALISATION OF DIGITAL FILTERS
HIGH SPEED REALISATION OF DIGITAL FILTERS A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF PHILOSOPHY IN ELECTRICAL AND ELECTRONIC ENGINEERING AT THE UNIVERSITY OF HONG KONG BY TSIM TS1M MAN-TAT, JIMMY DEPARTMENT
More informationFast Block LMS Adaptive Filter Using DA Technique for High Performance in FGPA
Fast Block LMS Adaptive Filter Using DA Technique for High Performance in FGPA Nagaraj Gowd H 1, K.Santha 2, I.V.Rameswar Reddy 3 1, 2, 3 Dept. Of ECE, AVR & SVR Engineering College, Kurnool, A.P, India
More informationInput parameters System specifics, user options. Input parameters size, dim,... FFT Code Generator. Initialization Select fastest execution plan
Automatic Performance Tuning in the UHFFT Library Dragan Mirković 1 and S. Lennart Johnsson 1 Department of Computer Science University of Houston Houston, TX 7724 mirkovic@cs.uh.edu, johnsson@cs.uh.edu
More informationSECURE DIGITAL COMMUNICATIONS
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 279 SECURE DIGITAL COMMUNICATIONS EDITED BY G. LONGO UNIVERSITA' DI TRIESTE SPRINGER-VERLAG WIEN GMBH This volume contains ll8 illustrations.
More informationTopological Structure and Analysis of Interconnection Networks
Topological Structure and Analysis of Interconnection Networks Network Theory and Applications Volume 7 Managing Editors: Ding-Zhu Du, University of Minnesota, U.S.A. and Cauligi Raghavendra, University
More informationSystem Demonstration of Spiral: Generator for High-Performance Linear Transform Libraries
System Demonstration of Spiral: Generator for High-Performance Linear Transform Libraries Yevgen Voronenko, Franz Franchetti, Frédéric de Mesmay, and Markus Püschel Department of Electrical and Computer
More informationDigital Signal Processing with Field Programmable Gate Arrays
Uwe Meyer-Baese Digital Signal Processing with Field Programmable Gate Arrays Third Edition With 359 Figures and 98 Tables Book with CD-ROM ei Springer Contents Preface Preface to Second Edition Preface
More informationGraphics Programming in c++
Graphics Programming in c++ Springer London Berlin Heidelberg New York Barcelona Budapest Hong Kong Milan Paris Santa Clara Singapore Tokyo Mark Walmsley Graphics Programming in c++ Writing Graphics Applications
More informationA Package for Generating, Manipulating, and Testing Convolution Algorithms. Anthony F. Breitzman and Jeremy R. Johnson
A Package for Generating, Manipulating, and Testing Convolution Algorithms Anthony F. Breitzman and Jeremy R. Johnson Technical Report DU-CS-03-05 Department of Computer Science Drexel University Philadelphia,
More informationPRIME FACTOR CYCLOTOMIC FOURIER TRANSFORMS WITH REDUCED COMPLEXITY OVER FINITE FIELDS
PRIME FACTOR CYCLOTOMIC FOURIER TRANSFORMS WITH REDUCED COMPLEXITY OVER FINITE FIELDS Xuebin Wu, Zhiyuan Yan, Ning Chen, and Meghanad Wagh Department of ECE, Lehigh University, Bethlehem, PA 18015 PMC-Sierra
More informationTHE VERILOG? HARDWARE DESCRIPTION LANGUAGE
THE VERILOG? HARDWARE DESCRIPTION LANGUAGE THE VERILOGf HARDWARE DESCRIPTION LANGUAGE by Donald E. Thomas Carnegie Mellon University and Philip R. Moorby Cadence Design Systems, Inc. SPRINGER SCIENCE+BUSINESS
More informationMATLAB Numerical Calculations. César Pérez López
MATLAB Numerical Calculations César Pérez López MATLAB Numerical Calculations Copyright 2014 by César Pérez López This work is subject to copyright. All rights are reserved by the Publisher, whether the
More informationScheduling in Distributed Computing Systems Analysis, Design & Models
Scheduling in Distributed Computing Systems Analysis, Design & Models (A Research Monograph) Scheduling in Distributed Computing Systems Analysis, Design & Models (A Research Monograph) by Deo Prakash
More informationOpen Geometry: OpenGL + Advanced Geometry
Open Geometry: OpenGL + Advanced Geometry Springer-Science+Business Media, LLC Open Geometry: OpenGL + Advanced Geometry Georg Glaeser Hellmuth Stachel Springer Georg G laeser University of Applied Arts,
More informationJinkun Liu Xinhua Wang. Advanced Sliding Mode Control for Mechanical Systems. Design, Analysis and MATLAB Simulation
Jinkun Liu Xinhua Wang Advanced Sliding Mode Control for Mechanical Systems Design, Analysis and MATLAB Simulation Jinkun Liu Xinhua Wang Advanced Sliding Mode Control for Mechanical Systems Design, Analysis
More informationMATLAB Programming for Numerical Analysis. César Pérez López
MATLAB Programming for Numerical Analysis César Pérez López MATLAB Programming for Numerical Analysis Copyright 2014 by César Pérez López This work is subject to copyright. All rights are reserved by the
More informationSymbolicC++: An Introduction to Computer Algebra using Object-Oriented Programming
SymbolicC++: An Introduction to Computer Algebra using Object-Oriented Programming Springer-Verlag London Ltd. Tan Kiat Shi, Willi-Hans Steeb and Yorick Hardy SymbolicC ++: An Introdurtion to Computer
More informationFunctional Programming in R
Functional Programming in R Advanced Statistical Programming for Data Science, Analysis and Finance Thomas Mailund Functional Programming in R: Advanced Statistical Programming for Data Science, Analysis
More informationComputer Science Workbench. Editor: Tosiyasu L. Kunii
Computer Science Workbench Editor: Tosiyasu L. Kunii H. Kitagawa T.L. Kunii The U nnortnalized Relational Data Model F or Office Form Processor Design With 78 Figures Springer-Verlag Tokyo Berlin Heidelberg
More informationDiscrete Mathematics SECOND EDITION OXFORD UNIVERSITY PRESS. Norman L. Biggs. Professor of Mathematics London School of Economics University of London
Discrete Mathematics SECOND EDITION Norman L. Biggs Professor of Mathematics London School of Economics University of London OXFORD UNIVERSITY PRESS Contents PART I FOUNDATIONS Statements and proofs. 1
More informationAdvanced Computing Research Laboratory. Adaptive Scientific Software Libraries
Adaptive Scientific Software Libraries and Texas Learning and Computation Center and Department of Computer Science University of Houston Challenges Diversity of execution environments Growing complexity
More informationCOMPUTATIONAL DYNAMICS
COMPUTATIONAL DYNAMICS THIRD EDITION AHMED A. SHABANA Richard and Loan Hill Professor of Engineering University of Illinois at Chicago A John Wiley and Sons, Ltd., Publication COMPUTATIONAL DYNAMICS COMPUTATIONAL
More informationStefan Waldmann. Topology. An Introduction
Topology Stefan Waldmann Topology An Introduction 123 Stefan Waldmann Julius Maximilian University of Würzburg Würzburg Germany ISBN 978-3-319-09679-7 ISBN 978-3-319-09680-3 (ebook) DOI 10.1007/978-3-319-09680-3
More information6. Fast Fourier Transform
x[] X[] x[] x[] x[6] X[] X[] X[3] x[] x[5] x[3] x[7] 3 X[] X[5] X[6] X[7] A Historical Perspective The Cooley and Tukey Fast Fourier Transform (FFT) algorithm is a turning point to the computation of DFT
More informationStock Message Boards
Stock Message Boards This page intentionally left blank Stock Message Boards A Quantitative Approach to Measuring Investor Sentiment Ying Zhang STOCK MESSAGE BOARDS Copyright Ying Zhang, 2014. Softcover
More informationLOGICAL DATA MODELING
LOGICAL DATA MODELING INTEGRATED SERIES IN INFORMATION SYSTEMS Professor Ramesh Sharda Oklahoma State University Series Editors Prof. Dr. Stefan VoB Universitat Hamburg Expository and Research Monographs
More informationARCHITECTURE AND CAD FOR DEEP-SUBMICRON FPGAs
ARCHITECTURE AND CAD FOR DEEP-SUBMICRON FPGAs THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE ARCHITECTURE AND CAD FOR DEEP-SUBMICRON FPGAs Vaughn Betz Jonathan Rose Alexander Marquardt
More informationPreface. and Its Applications 81, ISBN , doi: / , Springer Science+Business Media New York, 2013.
Preface This book is for all those interested in using the GAMS technology for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Mainly, it is a continuation
More informationMultidimensional Queueing Models in Telecommunication Networks
Multidimensional Queueing Models in Telecommunication Networks ThiS is a FM Blank Page Agassi Melikov Leonid Ponomarenko Multidimensional Queueing Models in Telecommunication Networks Agassi Melikov Department
More informationResearch on Industrial Security Theory
Research on Industrial Security Theory Menggang Li Research on Industrial Security Theory Menggang Li China Centre for Industrial Security Research Beijing, People s Republic of China ISBN 978-3-642-36951-3
More informationThe Verilog Hardware Description Language. Fifth Edition
The Verilog Hardware Description Language Fifth Edition Donald Thomas Philip Moorby The Verilog Hardware Description Language Fifth Edition Donald Thomas Carnegie Mellon University Pittsburgh, PA USA Philip
More informationAbstract. Literature Survey. Introduction. A.Radix-2/8 FFT algorithm for length qx2 m DFTs
Implementation of Split Radix algorithm for length 6 m DFT using VLSI J.Nancy, PG Scholar,PSNA College of Engineering and Technology; S.Bharath,Assistant Professor,PSNA College of Engineering and Technology;J.Wilson,Assistant
More informationMULTIMEDIA DATABASE MANAGEMENT SYSTEMS
MULTIMEDIA DATABASE MANAGEMENT SYSTEMS THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE MULTIMEDIA SYSTEMS AND APPLICATIONS Recently Published Titles: Consulting Editor Borko Furht Florida
More informationPERFORMANCE ANALYSIS OF REAL-TIME EMBEDDED SOFTWARE
PERFORMANCE ANALYSIS OF REAL-TIME EMBEDDED SOFTWARE PERFORMANCE ANALYSIS OF REAL-TIME EMBEDDED SOFTWARE Yau-Tsun Steven Li Monterey Design Systems, Inc. Sharad Malik Princeton University ~. " SPRINGER
More informationExcel for Chemists. Second Edition
Excel for Chemists Second Edition This page intentionally left blank ExceL for Chemists A Comprehensive Guide Second Edition E. Joseph Billo Department of Chemistry Boston College Chestnut Hill, Massachusetts
More informationAn efficient multiplierless approximation of the fast Fourier transform using sum-of-powers-of-two (SOPOT) coefficients
Title An efficient multiplierless approximation of the fast Fourier transm using sum-of-powers-of-two (SOPOT) coefficients Author(s) Chan, SC; Yiu, PM Citation Ieee Signal Processing Letters, 2002, v.
More informationMobile Phone Security and Forensics
Mobile Phone Security and Forensics Iosif I. Androulidakis Mobile Phone Security and Forensics A Practical Approach Second Edition Iosif I. Androulidakis Pedini Ioannina Greece ISBN 978-3-319-29741-5
More informationCOMPUTER VISION FOR VISUAL EFFECTS
COMPUTER VISION FOR VISUAL EFFECTS Modern blockbuster movies seamlessly introduce impossible characters and action into real-world settings using digital visual effects. These effects are made possible
More informationNew Syllabus Mathematics for 0-Level 1
New Syllabus Mathematics for 0-Level 1 New Syllabus Mathematics for 0-Level 1 New Syllabus Mathematics for 0-Level 2 New Syllabus Mathematics for 0-Levell Owen Perry, B.Sc., Head of Department of General
More informationTASK SCHEDULING FOR PARALLEL SYSTEMS
TASK SCHEDULING FOR PARALLEL SYSTEMS Oliver Sinnen Department of Electrical and Computer Engineering The University of Aukland New Zealand TASK SCHEDULING FOR PARALLEL SYSTEMS TASK SCHEDULING FOR PARALLEL
More informationFundamentals of Operating Systems. Fifth Edition
Fundamentals of Operating Systems Fifth Edition Fundamentals of Operating Systems A.M. Lister University of Queensland R. D. Eager University of Kent at Canterbury Fifth Edition Springer Science+Business
More informationAlgorithms and Parallel Computing
Algorithms and Parallel Computing Algorithms and Parallel Computing Fayez Gebali University of Victoria, Victoria, BC A John Wiley & Sons, Inc., Publication Copyright 2011 by John Wiley & Sons, Inc. All
More informationWhitestein Series in software Agent Technologies. About whitestein Technologies
Whitestein Series in software Agent Technologies Series Editors: Marius Walliser Stefan Brantschen Monique Calisti Thomas Hempfling This series reports new developments in agent-based software technologies
More informationJava Quick Syntax Reference. Second Edition. Mikael Olsson
Java Quick Syntax Reference Second Edition Mikael Olsson Java Quick Syntax Reference Second Edition Mikael Olsson Java Quick Syntax Reference Mikael Olsson Hammarland, Länsi-Suomi, Finland ISBN-13 (pbk):
More informationGuide to OSI and TCP/IP Models
SPRINGER BRIEFS IN COMPUTER SCIENCE Mohammed M. Alani Guide to OSI and TCP/IP Models SpringerBriefs in Computer Science Series editors Stan Zdonik Peng Ning Shashi Shekhar Jonathan Katz Xindong Wu Lakhmi
More informationINFORMATION RETRIEVAL SYSTEMS: Theory and Implementation
INFORMATION RETRIEVAL SYSTEMS: Theory and Implementation THE KLUWER INTERNATIONAL SERIES ON INFORMATION RETRIEVAL Series Editor W. Bruce Croft University of Massachusetts Amherst, MA 01003 Also in the
More informationFormal Loop Merging for Signal Transforms
Formal Loop Merging for Signal Transforms Franz Franchetti Yevgen S. Voronenko Markus Püschel Department of Electrical & Computer Engineering Carnegie Mellon University This work was supported by NSF through
More informationMULTIPLIERLESS HIGH PERFORMANCE FFT COMPUTATION
MULTIPLIERLESS HIGH PERFORMANCE FFT COMPUTATION Maheshwari.U 1, Josephine Sugan Priya. 2, 1 PG Student, Dept Of Communication Systems Engg, Idhaya Engg. College For Women, 2 Asst Prof, Dept Of Communication
More informationEfficient FFT Algorithm and Programming Tricks
Connexions module: m12021 1 Efficient FFT Algorithm and Programming Tricks Douglas L. Jones This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License Abstract
More informationAdaptive Scientific Software Libraries
Adaptive Scientific Software Libraries Lennart Johnsson Advanced Computing Research Laboratory Department of Computer Science University of Houston Challenges Diversity of execution environments Growing
More informationScheduling FFT Computation on SMP and Multicore Systems Ayaz Ali, Lennart Johnsson & Jaspal Subhlok
Scheduling FFT Computation on SMP and Multicore Systems Ayaz Ali, Lennart Johnsson & Jaspal Subhlok Texas Learning and Computation Center Department of Computer Science University of Houston Outline Motivation
More informationOpen Source Software for Digital Forensics
Open Source Software for Digital Forensics Ewa Huebner Editors Stefano Zanero Open Source Software for Digital Forensics Editors Ewa Huebner Computer Forensis Consulting, Warrimoo NSW Australia ehuebner@computerforensis.com
More informationScope and Sequence for the Maryland Voluntary State Curriculum for Mathematics
Scope and Sequence for the Maryland Voluntary State Curriculum for Mathematics The following chart provides an overview of where within Prentice Hall Course 1 Mathematics each of the Objectives of the
More informationChunjie Duan Brock J. LaMeres Sunil P. Khatri. On and Off-Chip Crosstalk Avoidance in VLSI Design
Chunjie Duan Brock J. LaMeres Sunil P. Khatri On and Off-Chip Crosstalk Avoidance in VLSI Design 123 On and Off-Chip Crosstalk Avoidance in VLSI Design Chunjie Duan Brock J. LaMeres Sunil P. Khatri On
More informationA Survey of Mathematics with Applications 8 th Edition, 2009
A Correlation of A Survey of Mathematics with Applications 8 th Edition, 2009 South Carolina Discrete Mathematics Sample Course Outline including Alternate Topics and Related Objectives INTRODUCTION This
More informationHIGH-SPEED COMMUNICATION NETWORKS
HIGH-SPEED COMMUNICATION NETWORKS HIGH-SPEED COMMUNICATION NETWORKS Edited by Harry Perros North Carolina State University Raleigh, North Carolina Springer Science+Busines s Media, LL C Library of Congress
More informationEncyclopedia of Information Science and Technology
Encyclopedia of Information Science and Technology Second Edition Mehdi Khosrow-Pour Information Resources Management Association, USA Volume IV G-Internet INFORMATION SCIENCE REFERENCE Hershey New York
More informationWindows 10 Revealed. The Universal Windows Operating System for PC, Tablets, and Windows Phone. Kinnary Jangla
Windows 10 Revealed The Universal Windows Operating System for PC, Tablets, and Windows Phone Kinnary Jangla Windows 10 Revealed Kinnary Jangla Bing Maps San Francisco, California, USA ISBN-13 (pbk): 978-1-4842-0687-4
More informationFFT. There are many ways to decompose an FFT [Rabiner and Gold] The simplest ones are radix-2 Computation made up of radix-2 butterflies X = A + BW
FFT There are many ways to decompose an FFT [Rabiner and Gold] The simplest ones are radix-2 Computation made up of radix-2 butterflies A X = A + BW B Y = A BW B. Baas 442 FFT Dataflow Diagram Dataflow
More informationDatabase Performance Tuning and Optimization. Using Oracle
Database Performance Tuning and Optimization Using Oracle Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo Sitansu S. Mittra Database Performance Tuning and Optimization Using Oracle
More informationGrade 4 CCSS Pacing Guide: Math Expressions
Grade 4 CCSS Pacing Guide: Math Expressions Green : Areas of intensive focus, where students need fluent understanding and application of the core concepts (Approximately 70%) Blue : Rethinking and linking;
More informationSOFTWARE-IMPLEMENTED HARDWARE FAULT TOLERANCE
SOFTWARE-IMPLEMENTED HARDWARE FAULT TOLERANCE SOFTWARE-IMPLEMENTED HARDWARE FAULT TOLERANCE O. Goloubeva, M. Rebaudengo, M. Sonza Reorda, and M. Violante Politecnico di Torino - Dipartimento di Automatica
More informationRectangular Matrix Multiplication Revisited
JOURNAL OF COMPLEXITY, 13, 42 49 (1997) ARTICLE NO. CM970438 Rectangular Matrix Multiplication Revisited Don Coppersmith IBM Research, T. J. Watson Research Center, Yorktown Heights, New York 10598 Received
More informationHandbook of Face Recognition
Handbook of Face Recognition Stan Z. Li Anil K. Jain Editors Handbook of Face Recognition With 210 Illustrations Stan Z. Li Anil K. Jain Center for Biometrics Research and Testing & Department of Computer
More informationChallenges of Computing the Fast Fourier. Transform. June 18, The Fast Fourier Transform, the FFT, discovered by Cooley and Tukey in 1964
Challenges of Computing the Fast Fourier Transform J. R. Johnson and R. W. Johnson June 18, 1997 1 Introduction The Fast Fourier Transform, the FFT, discovered by Cooley and Tukey in 1964 is one of most
More informationRadix-4 FFT Algorithms *
OpenStax-CNX module: m107 1 Radix-4 FFT Algorithms * Douglas L Jones This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 10 The radix-4 decimation-in-time
More informationTOPICS PIPELINE IMPLEMENTATIONS OF THE FAST FOURIER TRANSFORM (FFT) DISCRETE FOURIER TRANSFORM (DFT) INVERSE DFT (IDFT) Consulted work:
1 PIPELINE IMPLEMENTATIONS OF THE FAST FOURIER TRANSFORM (FFT) Consulted work: Chiueh, T.D. and P.Y. Tsai, OFDM Baseband Receiver Design for Wireless Communications, John Wiley and Sons Asia, (2007). Second
More informationComputer Science Workbench
Computer Science Workbench Editor: Tosiyasu L. Kunii Springer Japan KK Computer Science Workbench N. Magnenat Thalmann, D. Thalmann: Image Synthesis. Theory and Practice. XV, 400 pp., 223 figs., including
More informationAcademic Course Description
Academic Course Description SRM University Faculty of Engineering and Technology Department of Electronics and Communication Engineering VL2003 DSP Structures for VLSI Systems First Semester, 2014-15 (ODD
More informationSTEPHEN WOLFRAM MATHEMATICADO. Fourth Edition WOLFRAM MEDIA CAMBRIDGE UNIVERSITY PRESS
STEPHEN WOLFRAM MATHEMATICADO OO Fourth Edition WOLFRAM MEDIA CAMBRIDGE UNIVERSITY PRESS Table of Contents XXI a section new for Version 3 a section new for Version 4 a section substantially modified for
More informationAnalysis in Integer and Fractional Dimensions
Analysis in Integer and Fractional Dimensions Ron Blei University of Connecticut ^ i UNIVERSITY PRE^S Contents Preface Acknowledgements I A Prologue: Mostly Historical 1 1. From the Linear to the Bilinear
More informationSPIRAL Generated Modular FFTs *
SPIRAL Generated Modular FFTs * Jeremy Johnson Lingchuan Meng Drexel University * The work is supported by DARPA DESA, NSF, and Intel. Material for SPIRAL overview provided by Franz Francheti, Yevgen Voronenko,,
More informationComputer Communications and Networks. Series editor A.J. Sammes Centre for Forensic Computing Cranfield University, Shrivenham campus Swindon, UK
Computer Communications and Networks Series editor A.J. Sammes Centre for Forensic Computing Cranfield University, Shrivenham campus Swindon, UK The Computer Communications and Networks series is a range
More informationDIFFERENTIAL EQUATION ANALYSIS IN BIOMEDICAL SCIENCE AND ENGINEERING
DIFFERENTIAL EQUATION ANALYSIS IN BIOMEDICAL SCIENCE AND ENGINEERING DIFFERENTIAL EQUATION ANALYSIS IN BIOMEDICAL SCIENCE AND ENGINEERING ORDINARY DIFFERENTIAL EQUATION APPLICATIONS WITH R William E. Schiesser
More informationTheory of Automatic Robot Assembly and Programming
Theory of Automatic Robot Assembly and Programming Theory of Automatic Robot Assembly and Programming Bartholomew o. Nnaji Professor and Director Automation and Robotics Laboratory Department of Industrial
More informationSequence of Grade 4 Modules Aligned with the Standards
Sequence of Grade 4 Modules Aligned with the Standards Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction Module 2: Unit Conversions and Problem Solving with Metric Measurement
More informationEnergy Efficient Microprocessor Design
Energy Efficient Microprocessor Design Energy Efficient Microprocessor Design by Thomas D. Burd Robert W. Brodersen with Contributions Irom Trevor Pering Anthony Stratakos Berkeley Wireless Research Center
More informationA SIGNATURE ALGORITHM BASED ON DLP AND COMPUTING SQUARE ROOTS
A SIGNATURE ALGORITHM BASED ON DLP AND COMPUTING SQUARE ROOTS Ounasser Abid 1 and Omar Khadir 2 1, 2 Laboratory of Mathematics, Cryptography and Mechanics, FSTM University Hassan II of Casablanca, Morocco
More informationFFT ALGORITHMS FOR MULTIPLY-ADD ARCHITECTURES
FFT ALGORITHMS FOR MULTIPLY-ADD ARCHITECTURES FRANCHETTI Franz, (AUT), KALTENBERGER Florian, (AUT), UEBERHUBER Christoph W. (AUT) Abstract. FFTs are the single most important algorithms in science and
More informationSoftware Development for SAP R/3
Software Development for SAP R/3 Springer-Verlag Berlin Heidelberg GmbH Ulrich Mende Software Development for SAP R/3 Data Dictionary, ABAP/4, Interfaces With Diskette With 124 Figures and Many Example
More informationMATLAB. Advanced Mathematics and Mechanics Applications Using. Third Edition. David Halpern University of Alabama CHAPMAN & HALL/CRC
Advanced Mathematics and Mechanics Applications Using MATLAB Third Edition Howard B. Wilson University of Alabama Louis H. Turcotte Rose-Hulman Institute of Technology David Halpern University of Alabama
More informationJavaScript Essentials for SAP ABAP Developers
JavaScript Essentials for SAP ABAP Developers A Guide to Mobile and Desktop Application Development Rehan Zaidi JavaScript Essentials for SAP ABAP Developers: A Guide to Mobile and Desktop Application
More informationParallel string matching for image matching with prime method
International Journal of Engineering Research and Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 10, Issue 6 (June 2014), PP.42-46 Chinta Someswara Rao 1, 1 Assistant Professor,
More informationFourth Grade AKS Revisions For Common Core
Fourth Grade AKS Revisions For Common Core New AKS Aligned to Common Core Standards Explain a multiplication equation as a comparison and represent verbal statements of multiplicative comparisons as multiplication
More informationA Combined Encryption Compression Scheme Using Chaotic Maps
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 13, No 2 Sofia 2013 Print ISSN: 1311-9702; Online ISSN: 1314-4081 DOI: 10.2478/cait-2013-0016 A Combined Encryption Compression
More informationFPGA Based Design and Simulation of 32- Point FFT Through Radix-2 DIT Algorith
FPGA Based Design and Simulation of 32- Point FFT Through Radix-2 DIT Algorith Sudhanshu Mohan Khare M.Tech (perusing), Dept. of ECE Laxmi Naraian College of Technology, Bhopal, India M. Zahid Alam Associate
More informationThe Fast Fourier Transform Algorithm and Its Application in Digital Image Processing
The Fast Fourier Transform Algorithm and Its Application in Digital Image Processing S.Arunachalam(Associate Professor) Department of Mathematics, Rizvi College of Arts, Science & Commerce, Bandra (West),
More informationCryptography and Network Security
Cryptography and Network Security CRYPTOGRAPHY AND NETWORK SECURITY PRAKASH C. GUPTA Former Head Department of Information Technology Maharashtra Institute of Technology Pune Delhi-110092 2015 CRYPTOGRAPHY
More informationDISCRETE MATHEMATICS
DISCRETE MATHEMATICS WITH APPLICATIONS THIRD EDITION SUSANNA S. EPP DePaul University THOIVISON * BROOKS/COLE Australia Canada Mexico Singapore Spain United Kingdom United States CONTENTS Chapter 1 The
More information