Sampling and Quantization for Optimal Reconstruction by Shay Maymon Submitted to the Department of Electrical Engineering and Computer Science
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A Historical Perspective of Spectrum Estimation
PROCEEDINGSIEEE, OF THE VOL. 70, NO. 9, SEPTEMBER885 1982 A Historical Perspective of Spectrum Estimation ENDERS A. ROBINSON Invited Paper Alwhrct-The prehistory of spectral estimation has its mots in an- times, credit for the empirical discovery of spectra goes to the cient times with the development of the calendar and the clock The diversified genius of Sir Isaac Newton [ 11. But the great in- work of F’ythagom in 600 B.C. on the laws of musical harmony found mathematical expression in the eighteenthcentury in terms of the wave terest in spectral analysis made its appearanceonly a little equation. The strueto understand the solution of the wave equation more than a century ago. The prominent German chemist was fhlly resolved by Jean Baptiste Joseph de Fourier in 1807 with Robert Wilhelm Bunsen (18 1 1-1899) repeated Newton’s his introduction of the Fourier series TheFourier theory was ex- experiment of the glass prism. Only Bunsen did not use the tended to the case of arbitrary orthogollpl functions by Stmn and sun’s rays Newton did. Newtonhad found that aray of Liowillein 1836. The Stum+Liouville theory led to the greatest as empirical sum of spectral analysis yet obbhed, namely the formulo sunlight is expanded into a band of many colors, the spectrum tion of quantum mechnnics as given by Heisenberg and SchrMngm in of the rainbow. In Bunsen’s experiment, the role of pure sun- 1925 and 1926. In 1929 John von Neumann put the spectral theory of light was replaced by the burning of an old rag that had been the atom on a Turn mathematical foundation in his spectral represent, soaked in a salt solution (sodium chloride). -
Dsp Notes Prepared
DSP NOTES PREPARED BY Ch.Ganapathy Reddy Professor & HOD, ECE Shaikpet, Hyderabad-08 Ch Ganapathy Reddy, Prof and HOD, ECE, GNITS id:[email protected],9052344333 1 DIGITAL SIGNAL PROCESSING A signal is defined as any physical quantity that varies with time, space or another independent variable. A system is defined as a physical device that performs an operation on a signal. System is characterized by the type of operation that performs on the signal. Such operations are referred to as signal processing. Advantages of DSP 1. A digital programmable system allows flexibility in reconfiguring the digital signal processing operations by changing the program. In analog redesign of hardware is required. 2. In digital accuracy depends on word length, floating Vs fixed point arithmetic etc. In analog depends on components. 3. Can be stored on disk. 4. It is very difficult to perform precise mathematical operations on signals in analog form but these operations can be routinely implemented on a digital computer using software. 5. Cheaper to implement. 6. Small size. 7. Several filters need several boards in analog, whereas in digital same DSP processor is used for many filters. Disadvantages of DSP 1. When analog signal is changing very fast, it is difficult to convert digital form .(beyond 100KHz range) 2. w=1/2 Sampling rate. 3. Finite word length problems. 4. When the signal is weak, within a few tenths of millivolts, we cannot amplify the signal after it is digitized. 5. DSP hardware is more expensive than general purpose microprocessors & micro controllers. Ch Ganapathy Reddy, Prof and HOD, ECE, GNITS id:[email protected],9052344333 2 6. -
Hexagonal Structure for Intelligent Vision
© 2005 IEEE. Reprinted, with permission, from Xiangjian He, Hexagonal Structure for Intelligent Vision . Information and Communication Technologies, 2005. ICICT 2005. First International Conference on, August 2005. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Technology, Sydney's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs- [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it HEXAGONAL STRUCTURE FOR INTELLIGENT VISION Xiangjian He and Wenjing Jia Computer Vision Research Group Faculty of Information Technology University of Technology, Sydney Australia Abstract: greater angular resolution, and a reduced need of storage Using hexagonal grids to represent digital images has and computation in image processing operations. been studied for more than 40 years. Increased processing In spite of its numerous advantages, hexagonal grid has so capabilities of graphic devices and recent improvements in far not yet been widely used in computer vision and CCD technology have made hexagonal sampling graphics field. The main problem that limits the use of attractive for practical applications and brought new hexagonal image structure is believed due to lack of interests on this topic. The hexagonal structure is hardware for capturing and displaying hexagonal-based considered to be preferable to the rectangular structure images. -
Martin Gardner Receives JPBM Communications Award
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIAnON OF AMERICA Martin Gardner Receives JPBM voIome 14, Number 4 Communications Award Martin Gardner has been named the 1994 the United States Navy recipient of the Joint Policy Board for Math and served until the end ematics Communications Award. Author of of the Second World In this Issue numerous books and articles about mathemat War. He began his Sci ics' Gardner isbest known for thelong-running entific Americancolumn "Mathematical Games" column in Scientific in December 1956. 4 CD-ROM American. For nearly forty years, Gardner, The MAA is proud to count Gardneras one of its Textbooks and through his column and books, has exertedan authors. He has published four books with the enormous influence on mathematicians and Calculus Association, with three more in thepipeline. This students of mathematics. September, he begins "Gardner's Gatherings," 6 Open Secrets When asked about the appeal of mathemat a new column in Math Horizons. ics, Gardner said, "It's just the patterns, and Previous JPBM Communications Awards have their order-and their beauty: the way it all gone to James Gleick, author of Chaos; Hugh 8 Section Awards fits together so it all comes out right in the Whitemore for the play Breaking the Code; Ivars end." for Distinguished Peterson, author of several books and associate Teaching Gardner graduated Phi Beta Kappa in phi editor of Science News; and Joel Schneider, losophy from the University of Chicago in content director for the Children's Television 10 Personal Opinion 1936, and then pursued graduate work in the Workshop's Square One TV. -
Publications of Members, 1930-1954
THE INSTITUTE FOR ADVANCED STUDY PUBLICATIONS OF MEMBERS 1930 • 1954 PRINCETON, NEW JERSEY . 1955 COPYRIGHT 1955, BY THE INSTITUTE FOR ADVANCED STUDY MANUFACTURED IN THE UNITED STATES OF AMERICA BY PRINCETON UNIVERSITY PRESS, PRINCETON, N.J. CONTENTS FOREWORD 3 BIBLIOGRAPHY 9 DIRECTORY OF INSTITUTE MEMBERS, 1930-1954 205 MEMBERS WITH APPOINTMENTS OF LONG TERM 265 TRUSTEES 269 buH FOREWORD FOREWORD Publication of this bibliography marks the 25th Anniversary of the foundation of the Institute for Advanced Study. The certificate of incorporation of the Institute was signed on the 20th day of May, 1930. The first academic appointments, naming Albert Einstein and Oswald Veblen as Professors at the Institute, were approved two and one- half years later, in initiation of academic work. The Institute for Advanced Study is devoted to the encouragement, support and patronage of learning—of science, in the old, broad, undifferentiated sense of the word. The Institute partakes of the character both of a university and of a research institute j but it also differs in significant ways from both. It is unlike a university, for instance, in its small size—its academic membership at any one time numbers only a little over a hundred. It is unlike a university in that it has no formal curriculum, no scheduled courses of instruction, no commitment that all branches of learning be rep- resented in its faculty and members. It is unlike a research institute in that its purposes are broader, that it supports many separate fields of study, that, with one exception, it maintains no laboratories; and above all in that it welcomes temporary members, whose intellectual development and growth are one of its principal purposes. -
Noise Will Be Noise: Or Phase Optimized Recursive Filters for Interference Suppression, Signal Differentiation and State Estimation (Extended Version) Hugh L
Available online at https://arxiv.org/ 1 Noise will be noise: Or phase optimized recursive filters for interference suppression, signal differentiation and state estimation (extended version) Hugh L. Kennedy Abstract— The increased temporal and spectral resolution of oversampled systems allows many sensor-signal analysis tasks to be performed (e.g. detection, classification and tracking) using a filterbank of low-pass digital differentiators. Such filters are readily designed via flatness constraints on the derivatives of the complex frequency response at dc, pi and at the centre frequencies of narrowband interferers, i.e. using maximally-flat (MaxFlat) designs. Infinite-impulse-response (IIR) filters are ideal in embedded online systems with high data-rates because computational complexity is independent of their (fading) ‘memory’. A novel procedure for the design of MaxFlat IIR filterbanks with improved passband phase linearity is presented in this paper, as a possible alternative to Kalman and Wiener filters in a class of derivative-state estimation problems with uncertain signal models. Butterworth poles are used for configurable bandwidth and guaranteed stability. Flatness constraints of arbitrary order are derived for temporal derivatives of arbitrary order and a prescribed group delay. As longer lags (in samples) are readily accommodated in oversampled systems, an expression for the optimal group delay that minimizes the white-noise gain (i.e. the error variance of the derivative estimate at steady state) is derived. Filter zeros are optimally placed for the required passband phase response and the cancellation of narrowband interferers in the stopband, by solving a linear system of equations. Low complexity filterbank realizations are discussed then their behaviour is analysed in a Teager-Kaiser operator to detect pulsed signals and in a state observer to track manoeuvring targets in simulated scenarios. -
Overview Textbook Prerequisite Course Outline
ESE 337 Digital Signal Processing: Theory Fall 2018 Instructor: Yue Zhao Time and Location: Tuesday, Thursday 7:00pm - 8:20pm, Javits Lecture Center 101 Contact: Email: [email protected], Office: 261 Light Engineering Office Hours: Tuesday, Thursday 1:30pm - 3:00pm, or by appointment Teaching Assistants, and Office Hours: • Jiaming Li ([email protected]): THU 12:30pm - 2:00pm, or by appointment, Location: 208 Light Engineering (Changes of hours, if any, will be updated on Blackboard.) Overview Digital Signal Processing (DSP) lies at the heart of modern information technology in many fields including digital communications, audio/image/video compression, speech recognition, medical imaging, sensing for health, touch screens, space exploration, etc. This class covers the basic principles of digital signal processing and digital filtering. Skills for analyzing and synthesizing algorithms and systems that process discrete time signals will be developed. 3 credits. Textbook • A.V. Oppenheim and R.W. Schafer, Discrete Time Signal Processing, Prentice Hall, Third Edition, 2009 Prerequisite • ESE 305, Deterministic Signals and Systems Course Outline Week 1 DT signals, DT systems and properties, LTI systems Week 2 Convolution, properties of LTI systems Week 3 Examples of LTI systems, eigen functions, frequency response of DT systems, DTFT 1 ESE 337 Syllabus Week 4 Convergence and properties of DTFT Week 5 Theorems of DTFT, useful DTFT pairs, examples, Z-transform Week 6 Examples of Z-transform, properties of ROC Week 7 Inverse Z-transform, -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
Introducing the Mini-DML Project Thierry Bouche
Introducing the mini-DML project Thierry Bouche To cite this version: Thierry Bouche. Introducing the mini-DML project. ECM4 Satellite Conference EMANI/DML, Jun 2004, Stockholm, Sweden. 11 p.; ISBN 3-88127-107-4. hal-00347692 HAL Id: hal-00347692 https://hal.archives-ouvertes.fr/hal-00347692 Submitted on 16 Dec 2008 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Introducing the mini-DML project Thierry Bouche Université Joseph Fourier (Grenoble) WDML workshop Stockholm June 27th 2004 Introduction At the Göttingen meeting of the Digital mathematical library project (DML), in May 2004, the issue was raised that discovery and seamless access to the available digitised litterature was still a task to be acomplished. The ambitious project of a comprehen- sive registry of all ongoing digitisation activities in the field of mathematical research litterature was agreed upon, as well as the further investigation of many linking op- tions to ease user’s life. However, given the scope of those projects, their benefits can’t be expected too soon. Between the hope of a comprehensive DML with many eYcient entry points and the actual dissemination of heterogeneous partial lists of available material, there is a path towards multiple distributed databases allowing integrated search, metadata exchange and powerful interlinking. -
Understanding Digital Signal Processing
Understanding Digital Signal Processing Richard G. Lyons PRENTICE HALL PTR PRENTICE HALL Professional Technical Reference Upper Saddle River, New Jersey 07458 www.photr,com Contents Preface xi 1 DISCRETE SEQUENCES AND SYSTEMS 1 1.1 Discrete Sequences and Their Notation 2 1.2 Signal Amplitude, Magnitude, Power 8 1.3 Signal Processing Operational Symbols 9 1.4 Introduction to Discrete Linear Time-Invariant Systems 12 1.5 Discrete Linear Systems 12 1.6 Time-Invariant Systems 17 1.7 The Commutative Property of Linear Time-Invariant Systems 18 1.8 Analyzing Linear Time-Invariant Systems 19 2 PERIODIC SAMPLING 21 2.1 Aliasing: Signal Ambiquity in the Frequency Domain 21 2.2 Sampling Low-Pass Signals 26 2.3 Sampling Bandpass Signals 30 2.4 Spectral Inversion in Bandpass Sampling 39 3 THE DISCRETE FOURIER TRANSFORM 45 3.1 Understanding the DFT Equation 46 3.2 DFT Symmetry 58 v vi Contents 3.3 DFT Linearity 60 3.4 DFT Magnitudes 61 3.5 DFT Frequency Axis 62 3.6 DFT Shifting Theorem 63 3.7 Inverse DFT 65 3.8 DFT Leakage 66 3.9 Windows 74 3.10 DFT Scalloping Loss 82 3.11 DFT Resolution, Zero Padding, and Frequency-Domain Sampling 83 3.12 DFT Processing Gain 88 3.13 The DFT of Rectangular Functions 91 3.14 The DFT Frequency Response to a Complex Input 112 3.15 The DFT Frequency Response to a Real Cosine Input 116 3.16 The DFT Single-Bin Frequency Response to a Real Cosine Input 117 3.17 Interpreting the DFT 120 4 THE FAST FOURIER TRANSFORM 125 4.1 Relationship of the FFT to the DFT 126 4.2 Hints an Using FFTs in Practice 127 4.3 FFT Software Programs -
Multidimensional Sampling Dr
Multidimensional Sampling Dr. Vishal Monga Motivation for the General Case for Sampling We need the more general case to treat three important applications. 1. Human Vision System: the human vision system is a nonlinear, spatially- varying, non-uniformly sampled system. Rods and cones on the retina, which spatially sample are not arranged in rows and columns. a. Hexagonal Sampling: when modeled as a linear shift-invariant system, the human visual system is circularly bandlimited (lowpass in radial frequency). The optimal uniform sampling grid is hexagonal. Optimal means that we need the fewest discrete-time samples to sample the continuous-space analog signal without aliasing. b. Foveated grid: This is based on the fovea in the retina. When you focus on an object, you sample the object at a high resolution, and the resolution falls off away from the point-of-focus. Shown below is a simple example of a foveated grid. The grid is a 4 x 4 uniform sampling with each of the middle four grids subdivided into 4 x 4 grids themselves. The point of focus is at the middle of the grid. We can convert this grid to a uniform grid in several ways. For example, we could start with a rectangular grid and keep the resolution at the point-of-focus. Then, away from the point-of-focus, we can average the pixel values in increasingly larger blocks of samples. This approach allows the use a foveated grid while maintaining compatibility with systems that require rectangular sampling (e.g. image and video compression standards). 2. Television 650 samples /row 362.5 rows /interlace 2 interlaces /frame 30 frames /sec No two samples taken at the same instant of time Can signals be sampled this way without losing information? How can we handle a. -
ARRAY SET ADDRESSING: ENABLING EFFICIENT HEXAGONALLY SAMPLED IMAGE PROCESSING by NICHOLAS I. RUMMELT a DISSERTATION PRESENTED TO
ARRAY SET ADDRESSING: ENABLING EFFICIENT HEXAGONALLY SAMPLED IMAGE PROCESSING By NICHOLAS I. RUMMELT A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 1 °c 2010 Nicholas I. Rummelt 2 To my beautiful wife and our three wonderful children 3 ACKNOWLEDGMENTS Thanks go out to my family for their support, understanding, and encouragement. I especially want to thank my advisor and committee chair, Joseph N. Wilson, for his keen insight, encouragement, and excellent guidance. I would also like to thank the other members of my committee: Paul Gader, Arunava Banerjee, Jeffery Ho, and Warren Dixon. I would like to thank the Air Force Research Laboratory (AFRL) for generously providing the opportunity, time, and funding. There are many people at AFRL that played some role in my success in this endeavor to whom I owe a debt of gratitude. I would like to specifically thank T.J. Klausutis, Ric Wehling, James Moore, Buddy Goldsmith, Clark Furlong, David Gray, Paul McCarley, Jimmy Touma, Tony Thompson, Marta Fackler, Mike Miller, Rob Murphy, John Pletcher, and Bob Sierakowski. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................. 4 LIST OF TABLES ...................................... 7 LIST OF FIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1 INTRODUCTION AND BACKGROUND ...................... 11 1.1 Introduction ................................... 11 1.2 Background ................................... 11 1.3 Recent Related Research ........................... 15 1.4 Recent Related Academic Research ..................... 16 1.5 Hexagonal Image Formation and Display Considerations ......... 17 1.5.1 Converting from Rectangularly Sampled Images .......... 17 1.5.2 Hexagonal Imagers ..........................