Introduction to Uniform Circular Motion and Gravitation

Introduction to Uniform Circular Motion and Gravitation tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập...

TEAM LinG INTRODUCTION TODIGITAL SIGNALPROCESSING ANDFILTER DESIGN INTRODUCTION TODIGITAL SIGNALPROCESSING ANDFILTER DESIGNB. A. ShenoiA JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2006 by John Wiley & Sons, Inc. All rights reserved.Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.No part of this publication may be reproduced, stored in a retrieval system, or transmitted in anyform or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, withouteither the prior written permission of the Publisher, or authorization through payment of theappropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requeststo the Publisher for permission should be addressed to the Permissions Department, John Wiley &Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online athttp://www.wiley.com/go/permission.Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their bestefforts in preparing this book, they make no representations or warranties with respect to theaccuracy or completeness of the contents of this book and specifically disclaim any impliedwarranties of merchantability or fitness for a particular purpose. No warranty may be created orextended by sales representatives or written sales materials. The advice and strategies containedherein may not be suitable for your situation. You should consult with a professional whereappropriate. Neither the publisher nor author shall be liable for any loss of profit or any othercommercial damages, including but not limited to special, incidental, consequential, or otherdamages.For general information on our other products and services or for technical support, please contactour Customer Care Department within the United States at (800) 762-2974, outside the UnitedStates at (317) 572-3993 or fax (317) 572-4002.Wiley also publishes its books in a variety of electronic formats. Some content that appears in printmay not be available in electronic formats. For more information about Wiley products, visit ourweb site at www.wiley.com.Library of Congress Cataloging-in-Publication Data:ISBN-13 978-0-471-46482-2 (cloth)Printed in the United States of America.10987654321ISBN-100-471- 46482-1 (cloth) CONTENTSPreface xi1 Introduction 11.1 Introduction 11.2 Applications of DSP 11.3 Discrete-Time Signals 31.3.1 Modeling and Properties of Discrete-Time Signals 81.3.2 Unit Pulse Function 91.3.3 Constant Sequence 101.3.4 Unit Step Function 101.3.5 Real Exponential Function 121.3.6 Complex Exponential Function 121.3.7 Properties of cos(ω0n) 141.4 History of Filter Design 191.5 Analog and Digital Signal Processing 231.5.1 Operation of a Mobile Phone Network 251.6 Summary 28Problems 29References 302 Time-Domain Analysis and z Transform 322.1 A Linear, Time-Invariant System 322.1.1 Models of the Discrete-Time System 332.1.2 Recursive Algorithm 362.1.3 Convolution Sum 382.2 z Transform Theory 412.2.1 Definition 412.2.2 Zero Input and Zero State Response 49v viCONTENTS2.2.3 Linearity of the System 502.2.4 Time-Invariant System 502.3 Using z Transform to Solve Difference Equations 512.3.1 More Applications of z Transform 562.3.2 Natural Response and Forced Response 582.4 Solving Difference Equations Using the Classical Method 592.4.1 Transient Response and Steady-State Response 632.5 z Transform Method Revisited 642.6 Convolution Revisited 652.7 A Model from Other Models 702.7.1 Review of Model Generation 722.8 Stability 772.8.1 Jury–Marden Test 782.9 Solution Using MATLAB Functions 812.10 Summary 93Problems Introduction to Uniform Circular Motion and Gravitation Introduction to Uniform Circular Motion and Gravitation Bởi: OpenStaxCollege This Australian Grand Prix Formula race car moves in a circular path as it makes the turn Its wheels also spin rapidly—the latter completing many revolutions, the former only part of one (a circular arc) The same physical principles are involved in each (credit: Richard Munckton) Many motions, such as the arc of a bird’s flight or Earth’s path around the Sun, are curved Recall that Newton’s first law tells us that motion is along a straight line at constant speed unless there is a net external force We will therefore study not only motion along curves, but also the forces that cause it, including gravitational forces In some ways, this chapter is a continuation of Dynamics: Newton's Laws of Motion as we study more applications of Newton’s laws of motion This chapter deals with the simplest form of curved motion, uniform circular motion, motion in a circular path at constant speed Studying this topic illustrates most concepts associated with rotational motion and leads to the study of many new topics we group under the name rotation Pure rotational motion occurs when points in an object move 1/2 Introduction to Uniform Circular Motion and Gravitation in circular paths centered on one point Pure translational motion is motion with no rotation Some motion combines both types, such as a rotating hockey puck moving along ice 2/2 TLFeBOOK Introduction to Logistics Systems Planning and Control TLFeBOOK WILEY-INTERSCIENCE SERIES IN SYSTEMS AND OPTIMIZATION Advisory Editors Sheldon Ross Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA Richard Weber Statistical Laboratory, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 0WB BATHER – Decision Theory: An Introduction to Dynamic Programming and Sequential Decisions CHAO/MIYAZAWA/PINEDO – Queueing Networks: Customers, Signals and Product Form Solutions COURCOUBETIS/WEBER – Pricing Communication Networks: Economics, Technology and Modelling DEB – Multi-Objective Optimization using Evolutionary Algorithms GERMAN – Performance Analysis of Communication Systems: Modeling with Non-Markovian Stochastic Petri Nets GHIANI/LAPORTE/MUSMANNO – Introduction to Logistics Systems Planning and Control KALL/WALLACE – Stochastic Programming KAMP/HASLER – Recursive Neural Networks for Associative Memory KIBZUN/KAN – Stochastic Programming Problems with Probability and Quantile Functions RUSTEM – Algorithms for Nonlinear Programming and Multiple-Objective Decisions WHITTLE – Optimal Control: Basics and Beyond WHITTLE – Neural Nets and Chaotic Carriers The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automation theory, operational research and industry. The more definite concept of a large-scale system is implicit in these applications, but is particularly evident in such fields as the study of communication networks, computer networks, and neural networks. The Wiley-Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with the developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. TLFeBOOK Introduction to Logistics Systems Planning and Control Gianpaolo Ghiani Department of Innovation Engineering, University of Lecce, Italy Gilbert Laporte Canada Research Chair in Distribution Management, HEC Montr´eal, Canada Roberto Musmanno Department of Electronics, Informatics and Systems, University of Calabria, Italy TLFeBOOK Copyright © 2004 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Phone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770571. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If CHAPTER 1 Introduction 1.1 INTRODUCTION We are living in an age of information technology. Most of this technology is based on the theory of digital signal processing (DSP) and implementation of the theory by devices embedded in what are known as digital signal processors (DSPs). Of course, the theory of digital signal processing and its applications is supported by other disciplines such as computer science and engineering, and advances in technologies such as the design and manufacturing of very large scale integration (VLSI) chips. The number of devices, systems, and applications of digital signal processing currently affecting our lives is very large and there is no end to the list of new devices, systems, and applications expected to be introduced into the market in the coming years. Hence it is difficult to forecast the future of digital signal processing and the impact of information technology. Some of the current applications are described below. 1.2 APPLICATIONS OF DSP Digital signal processing is used in several areas, including the following: 1. Telecommunications. Wireless or mobile phones are rapidly replacing wired (landline) telephones, both of which are connected to a large-scale telecom- munications network. They are used for voice communication as well as data communications. So also are the computers connected to a different network that is used for data and information processing. Computers are used to gen- erate, transmit, and receive an enormous amount of information through the Internet and will be used more extensively over the same network, in the com- ing years for voice communications also. This technology is known as voice over Internet protocol (VoIP) or Internet telephony. At present we can transmit and receive a limited amount of text, graphics, pictures, and video images from Introduction to Digital Signal Processing and Filter Design, by B. A. Shenoi Copyright © 2006 John Wiley & Sons, Inc. 1 2 INTRODUCTION mobile phones, besides voice, music, and other audio signals—all of which are classified as multimedia—because of limited hardware in the mobile phones and not the software that has already been developed. However, the computers can be used to carry out the same functions more efficiently with greater memory and large bandwidth. We see a seamless integration of wireless telephones and com- puters already developing in the market at present. The new technologies being used in the abovementioned applications are known by such terms as CDMA, TDMA, 1 spread spectrum, echo cancellation, channel coding, adaptive equaliza- tion, ADPCM coding, and data encryption and decryption, some of which are used in the software to be introduced in the third-generation (G3) mobile phones. 2. Speech Processing. The quality of speech transmission in real time over telecommunications networks from wired (landline) telephones or wireless (cel- lular) telephones is very high. Speech recognition, speech synthesis, speaker verification, speech enhancement, text-to-speech translation, and speech-to-text dictation are some of the other applications of speech processing. 3. Consumer Electronics. We have already mentioned cellular or mobile phones. Then we have HDTV, digital cameras, digital phones, answering machines, fax and modems, music synthesizers, recording and mixing of music signals to produce CD and DVDs. Surround-sound entertainment systems includ- ing CD and DVD players, laser printers, copying machines, and scanners are found in many homes. But the TV set, PC, PREFACE This preface is addressed to instructors as well as students at the junior–senior level for the following reasons. I have been teaching courses on digital signal processing, including its applications and digital filter design, at the undergraduate and the graduate levels for more than 25 years. One common complaint I have heard from undergraduate students in recent years is that there are not enough numerical problems worked out in the chapters of the book prescribed for the course. But some of the very well known textbooks on digital signal processing have more problems than do a few of the books published in earlier years. However, these books are written for students in the senior and graduate levels, and hence the junior-level students find that there is too much of mathematical theory in these books. They also have concerns about the advanced level of problems found at the end of chapters. I have not found a textbook on digital signal processing that meets these complaints and concerns from junior-level students. So here is a book that I have written to meet the junior students’ needs and written with a student-oriented approach, based on many years of teaching courses at the junior level. Network Analysis is an undergraduate textbook authored by my Ph.D. thesis advisor Professor M. E. Van Valkenburg (published by Prentice-Hall in 1964), which became a world-famous classic, not because it contained an abundance of all topics in network analysis discussed with the rigor and beauty of mathematical theory, but because it helped the students understand the basic ideas in their sim- plest form when they took the first course on network analysis. I have been highly influenced by that book, while writing this textbook for the first course on digital signal processing that the students take. But I also have had to remember that the generation of undergraduate students is different; the curriculum and the topic of digital signal processing is also different. This textbook does not contain many of the topics that are found in the senior–graduate-level textbooks mentioned above. One of its main features is that it uses a very large number of numerical problems as well as problems using functions from MATLAB ® (MATLAB is a registered trademark of The MathWorks, Inc.) and Signal Processing Toolbox, worked out in every chapter, in order to highlight the fundamental concepts. These prob- lems are solved as examples after the theory is discussed or are worked out first and the theory is then presented. Either way, the thrust of the approach is that the students should understand the basic ideas, using the worked, out problems as an instrument to achieve that goal. In some cases, the presentation is more informal than in other cases. The students will find statements beginning with “Note that .,” “Remember .,” or “It is pointed out,” and so on; they are meant xi xii PREFACE to emphasize the important concepts and the results stated in those sentences. Many of the important results are mentioned more than once or summarized in order to emphasize their significance. The other attractive feature of this book is that all the problems given at the end of the chapters are problems that can be solved by using only the material discussed in the chapters, so that students would feel confident that they have an understanding of the material covered in the course when they succeed in solving the problems. Because of such considerations mentioned above, the author claims that the book is written with a student-oriented approach. Yet, the students should know that the ability to understand the solution to the problems is important but understanding the theory behind 1 IDIC – SANS GIAC LevelTwo ©2000, 2001 1 Network Based Intrusion Detection Tutorial 1 Introduction to the basic approaches and issues of Intrusion Detection Hello! Welcome to the first half of our network based intrusion detection tutorial, where we will introduce you to the basic approaches of intrusion detection. In this section, we will discuss a rule- based analysis process by going through the topics listed on your next slide. At the end of the section we will talk about some of the methods currently used to perform intrusion detection. 2 IDIC - SANS GIAC LevelTwo ©2000, 2001 2 • False positives, False negatives • EOI, dictionary signatures, profile changes • Severity = (criticality + lethality) – countermeasures (system + network) • Long term conditions Before We Begin We will begin our discussion by talking about false positives and false negatives, which are ever present factors in the life of an intrusion analyst. We will then discuss the notion of Events of Interest (EOI), and their relevance to the event analysis process. We will also go over techniques for judging the severity of a particular event. Additionally, we will propose a way to handle long term conditions that might result from a prolonged exposure to attacks. 3 IDIC - SANS GIAC LevelTwo ©2000, 2001 3 Sources of Data All data: observable or not Collectable Events of Interest There are very few situations in which we are able to collect all the data. We need to develop techniques that allow us to routinely locate Events of Interest (EOI) in the data we are able to collect, so that we know where to focus our attention. 4 IDIC - SANS GIAC LevelTwo ©2000, 2001 4 False Positives and Negatives False positives False negatives All Data Real EOI False positives are “false alarms.” The detects match only some of the criteria for indicators of possible intrusion. False positives tend to wear down incident handling resources and make us slower to react in the future. False negatives are the actual intrusions and intrusion attempts that we do not detect. These can allow an adversary to establish a significant presence in our information systems before we begin to react. 5 IDIC - SANS GIAC LevelTwo ©2000, 2001 5 What Are Events Of Interest • Since we can’t collect, store, or analyze all possible events, we focus our collection efforts on stuff that might prove useful, EOI. – Dictionary: known attack signatures, known attackers – Short term significant changes in system or user profile The reality of limited computing and personnel resources is such that we cannot collect, store, and analyze all possible events. Therefore, analysts tend to focus their collection efforts on events that might prove useful – Events of Interest (EOI). Unfortunately, focusing helps reduce the false alarms or false positives, but increases the chance of missing an EOI. One of the ways to help ensure that an EOI is not missed is to compare suspicious events against a dictionary of known attacks or attackers. You can’t afford not to test against a dictionary! Another way to widen our field of vision is to monitor for changes in system or user profiles. Consider the following example: You have noticed an increase in the number of probes and intrusion attempts at your site. DNS and mail relay systems are always high profile targets, so you are .. .Introduction to Uniform Circular Motion and Gravitation in circular paths centered on one point Pure translational motion is motion with no rotation Some motion combines both