1 Introduction to Real-Time Digital Signal Processing Signals can be divided into three categories ± continuous-time (analog) signals, discrete-time signals, and digital signals. The signals that we encounter daily are mostly analog signals. These signals are defined continuously in time, have an infinite range of amplitude values, and can be processed using electrical devices containing both active and passive circuit elements. Discrete-time signals are defined only at a particular set of time instances. Therefore they can be represented as a sequence of numbers that have a continuous range of values. On the other hand, digital signals have discrete values in both time and amplitude. In this book, we design and implement digital systems for processing digital signals using digital hardware. However, the analysis of such signals and systems usually uses discrete-time signals and systems for math- ematical convenience. Therefore we use the term `discrete-time' and `digital' inter- changeably. Digital signal processing (DSP) is concerned with the digital representation of signals and the use of digital hardware to analyze, modify, or extract information from these signals. The rapid advancement in digital technology in recent years has created the implementation of sophisticated DSP algorithms that make real-time tasks feasible. A great deal of research has been conducted to develop DSP algorithms and applications. DSP is now used not only in areas where analog methods were used previously, but also in areas where applying analog techniques is difficult or impossible. There are many advantages in using digital techniques for signal processing rather than traditional analog devices (such as amplifiers, modulators, and filters). Some of the advantages of a DSP system over analog circuitry are summarized as follows: 1. Flexibility. Functions of a DSP system can be easily modified and upgraded with software that has implemented the specific algorithm for using the same hardware. One can design a DSP system that can be programmed to perform a wide variety of tasks by executing different software modules. For example, a digital camera may be easily updated (reprogrammed) from using JPEG ( joint photographic experts group) image processing to a higher quality JPEG2000 image without actually changing the hardware. In an analog system, however, the whole circuit design would need to be changed. Real-Time Digital Signal Processing. Sen M Kuo, Bob H Lee Copyright # 2001 John Wiley & Sons Ltd ISBNs: 0-470-84137-0 (Hardback); 0-470-84534-1 (Electronic) 2. Reproducibility. The performance of a DSP system can be repeated precisely from one unit to another. This is because the signal processing of DSP systems work directly with binary sequences. Analog circuits will not perform as well from each circuit, even if they are built following identical specifications, due to component tolerances in analog components. In addition, by using DSP techniques, a digital signal can be transferred or reproduced many times without degrading its signal quality. 3. Reliability. The memory and logic of DSP hardware does not deteriorate with age. Therefore the field performance of DSP systems will not drift with changing environmental conditions or aged electronic components as their analog counter- parts do. However, the data size (wordlength) determines the accuracy of a DSP system. Thus the system performance might be different from the theoretical expect- ation. 4. Complexity. Using DSP allows sophisticated applications such as speech or image recognition to be implemented for lightweight and low power portable devices. This is impractical using traditional analog Adjusting Nominal Values to Real Values Adjusting Nominal Values to Real Values By: OpenStaxCollege When examining economic statistics, there is a crucial distinction worth emphasizing The distinction is between nominal and real measurements, which refer to whether or not inflation has distorted a given statistic Looking at economic statistics without considering inflation is like looking through a pair of binoculars and trying to guess how close something is: unless you know how strong the lenses are, you cannot guess the distance very accurately Similarly, if you not know the rate of inflation, it is difficult to figure out if a rise in GDP is due mainly to a rise in the overall level of prices or to a rise in quantities of goods produced The nominal value of any economic statistic means the statistic is measured in terms of actual prices that exist at the time The real value refers to the same statistic after it has been adjusted for inflation Generally, it is the real value that is more important Converting Nominal to Real GDP [link] shows U.S GDP at five-year intervals since 1960 in nominal dollars; that is, GDP measured using the actual market prices prevailing in each stated year This data is also reflected in the graph shown in [link] U.S Nominal GDP and the GDP Deflator(Source: www.bea.gov) Year Nominal GDP (billions of dollars) GDP Deflator (2005 = 100) 1960 543.3 19.0 1965 743.7 20.3 1970 1,075.9 24.8 1975 1,688.9 34.1 1980 2,862.5 48.3 1985 4,346.7 62.3 1/9 Adjusting Nominal Values to Real Values Year Nominal GDP (billions of dollars) GDP Deflator (2005 = 100) 1990 5,979.6 72.7 1995 7,664.0 81.7 2000 10,289.7 89.0 2005 13,095.4 100.0 2010 14,958.3 110.0 U.S Nominal GDP, 1960–2010 Nominal GDP values have risen exponentially from 1960 through 2010, according to the BEA If an unwary analyst compared nominal GDP in 1960 to nominal GDP in 2010, it might appear that national output had risen by a factor of twenty-seven over this time (that is, GDP of $14,958 billion in 2010 divided by GDP of $543 billion in 1960) This conclusion would be highly misleading Recall that nominal GDP is defined as the quantity of every good or service produced multiplied by the price at which it was sold, summed up for all goods and services In order to see how much production has actually increased, we need to extract the effects of higher prices on nominal GDP This can be easily done, using the GDP deflator GDP deflator is a price index measuring the average prices of all goods and services included in the economy We explore price indices in detail and how they are computed in Inflation, but this definition will in the context of this chapter The data for the GDP deflator are given in [link] and shown graphically in [link] 2/9 Adjusting Nominal Values to Real Values U.S GDP Deflator, 1960–2010 Much like nominal GDP, the GDP deflator has risen exponentially from 1960 through 2010 (Source: BEA) [link] shows that the price level has risen dramatically since 1960 The price level in 2010 was almost six times higher than in 1960 (the deflator for 2010 was 110 versus a level of 19 in 1960) Clearly, much of the apparent growth in nominal GDP was due to inflation, not an actual change in the quantity of goods and services produced, in other words, not in real GDP Recall that nominal GDP can rise for two reasons: an increase in output, and/or an increase in prices What is needed is to extract the increase in prices from nominal GDP so as to measure only changes in output After all, the dollars used to measure nominal GDP in 1960 are worth more than the inflated dollars of 1990—and the price index tells exactly how much more This adjustment is easy to if you understand that nominal measurements are in value terms, where Value = Price × Quantity or Nominal GDP = GDP Deflator × Real GDP Let’s look at an example at the micro level Suppose the t-shirt company, Coolshirts, sells 10 t-shirts at a price of $9 each Coolshirt's nominal revenue from sales = Price × Quantity = $9 × 10 = $90 Then, 3/9 Adjusting Nominal Values to Real Values Coolshirt's real income = Nominal revenue Price = $90 $9 = 10 In other words, when we compute “real” measurements we are trying to get at actual quantities, in this case, 10 t-shirts With GDP, it is just a tiny bit more complicated We start with the same formula as above: Real GDP = Nominal GDP Price Index For reasons that will be explained in more detail below, mathematically, a price index is a two-digit decimal number like 1.00 or 0.85 or 1.25 Because some people have trouble working with decimals, when the price index is published, it has traditionally been multiplied by 100 to get integer numbers like 100, 85, or 125 What this means is that when we “deflate” nominal figures to get real figures (by dividing the nominal by the price index) We also need to remember to divide the published price index by 100 to make the math work So the formula becomes: Real GDP = Nominal GDP Price Index / 100 Now read the ... C USTOMER T HINK G UIDE TO R EAL CRM P UTTING CUSTOMERS AT THE HEART OF YOUR BUSINESS. P ROFITABLY. January 2003 Published by © 2003 CustomerThink Corporation. All Rights Reserved. Reproduction and Distribution Strictly Prohibited. For reprint permission and fees, email reprint@crmguru.com . CustomerThink Guide to Real CRM Welcome to the CRMGuru Community! Thanks for becoming a member of CRMGuru.com, the world’s largest online community for Customer Relationship Management (CRM). Your fellow members are business managers and professionals who place “customers at the heart of business.” Our goal is to offer you exceptional content and advice on “Real CRM”—what we call CustomerThink—so that you can guide your CRM program on the road to success. We want to make you think and encourage you to challenge our thinking too! It allows us all to learn and grow as we take the customer-centric journey together. This CustomerThink Guide to Real CRM showcases a few articles to help you get started. But there’s much more. If you’re serious about CRM, invest some time exploring CRMGuru’s knowledgebase—known as the Gurubase 1 —which contains hundreds of archived articles, newsletters, discussions, and white papers. All designed to help you practice Real CRM. After you’ve finished this document, dig deeper by reading GuruBase articles covering: • Fundamentals of CRM, written by our expert panel 2 • Independent reviews of major CRM solutions 3 Again, welcome. We’ll do our best to make your CRMGuru experience enjoyable and educational. Let me know how we can help you on your Real CRM journey. Sincerely, Carol Parenzan Smalley Managing Editor, CRMGuru.com carol@crmguru.com 1 Go to www.crmguru.com/gurubase. 2 Go to http://www.crmguru.com/gurubase/basics.html 3 Go to http://www.crmguru.com/gurubase/solutions.html © 2003 CustomerThink Corporation CustomerThink Guide to Real CRM Table of Contents What is CRM? 1 Why Climb The CRM Mountain? 4 Build Value For Customers To Create Lasting Relationships 7 Great CRM Hinges on Great Business Processes 10 The Human Dimension: The Key to Success or Failure 13 A Guide to Evaluating CRM Software 14 Glossary of Commonly-Used CRM Terms 19 © 2003 CustomerThink Corporation CustomerThink Guide to Real CRM 1 W HAT IS CRM? By Bob Thompson The ideas behind customer relationship management are not new. Today it’s widely acknowledged that how you treat your customers goes a long way to determining your future profitability, and companies are making bigger and bigger investments to do just that. Customers are savvier about the service they should be getting and are voting with their wallets based on the experience they receive. The concepts of Customer Relationship Management have been in the air ever since one caveman had a choice of buying an arrowhead from either Og or Thag, but CRM as a term gained currency in the mid- 1990s. Market analysts squabble over the exact figure, but all agree that in the next few years companies will pour billions of dollars into CRM solutions—software and services designed to help businesses more effectively manage customer relationships through any direct or indirect channel a customer opts INTRODUCTION TO REAL ANALYSIS William F. Trench Professor Emeritus Department of Mathematics Trinity University San Antoni o, Texas, USA wtrench@trinity.edu FREE DOWNLOADABLE SUPPLEMENTS FUNCTIONS DEFINED BY IMPROPER INTEGRALS THE METHOD OF LAGRANGE MULT IPLIERS ©2003 William F. Trench, all rights reserved Library of Congress Cataloging-in-Publication Data Trench, William F. Introduction to real analysis / William F. Trench p. cm. ISBN 0-13-045786-8 1. Mathematical Analysis. I. Title. QA300.T667 2003 515-dc21 2002032369 Free Hyperlinked Edition 2.03, November 2012 This book was published previously by Pearson Education. This free edition is made available in the hope that it will be useful as a textbook or refer- ence. Reproduct ion is permitted for any valid noncommercial educational, mathematical, or scientific purpose. However, charges for profit beyond reasonable printing costs are prohibited. A complete instructor’s solution manual is available by email to wtrench@trinity.edu, sub- ject to verification of the requestor’s faculty status. TO BEVERLY Cont ents Preface vi Chapter 1 The Real Numbers 1 1.1 The Real Number System 1 1.2 Mathematical Induction 10 1.3 The Real Line 19 Chapter 2 Differential Calculus of Functions of One Varia ble 30 2.1 Functions and Lim its 30 2.2 Continuity 53 2.3 Di fferentiable Functions of One Variable 73 2.4 L’Hospital’s Rule 88 2.5 Taylor’s Theorem 98 Chapter 3 Integral Calculus of Functions of One Variable 113 3.1 Definition of the Integral 113 3.2 Existence of the Integral 128 3.3 Properties of the Integral 135 3.4 Improper Integrals 151 3.5 A More Advanced L ook at the Existence of the Proper Riemann Integral 171 Chapter 4 Infinite Sequences and Series 178 4.1 Sequences of Real Numbers 179 4.2 Earlier Topics Revisited With Sequences 195 4.3 Infinite Series of Constants 200 iv Contents v 4.4 Sequences and Series of Functions 234 4.5 Power Series 257 Chapter 5 Real-Valued Functions of Several Variables 281 5.1 Structure of R R R n 281 5.2 Continuous Real-Valued Function of n Variables 302 5.3 Partial Derivatives and the Differential 316 5.4 The Chain Rule and Taylor’ s Theorem 339 Chapter 6 Vector-Valued Functions of Several Variables 361 6.1 Linear Transformations and Matrices 361 6.2 Continuity and Differentiability of Transformations 378 6.3 The Inverse Function Theorem 394 6.4. The Implicit Function Theorem 417 Chapter 7 Integrals of Functions of Several Variables 435 7.1 Definition and Existence of the Multiple Integral 435 7.2 Iterated Integrals and Multiple Integrals 462 7.3 Change of Variables in Multiple Integrals 484 Chapter 8 Metric Spaces 518 8.1 Introduction to Metric Spaces 518 8.2 Compact Sets in a Metric Space 535 8.3 Continuous Functions on Metric Spaces 543 Answers to Selected Exercises 549 Index 563 Preface This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from t he mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fil l the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, ot her analysis oriented courses, such as elementary differential equa- tion, also provide useful preparatory experience.) Chapters 6 and 7 require a worki ng knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completi on of RECENT ADVANCES ON META-HEURISTICS AND THEIR APPLICATION TO REAL SCENARIOS Edited by Javier Del Ser Recent Advances on Meta-Heuristics and Their Application to Real Scenarios http://dx.doi.org/10.5772/3434 Edited by Javier Del Ser Contributors Fernando Francisco Sandoya, Dalessandro Vianna, Igor Carlos Pulini, Carlos Bazilio Martins, Alejandra Cruz-Bernal, Ikou Kaku, Patrick Siarry, Cédric Leboucher, Hyo-Sang Shin, Stéphane Le Ménec, Antonios Tsourdos, Rachid Chelouah Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2013 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Natalia Reinic Technical Editor InTech DTP team Cover InTech Design team First published January, 2013 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechopen.com Recent Advances on Meta-Heuristics and Their Application to Real Scenarios, Edited by Javier Del Ser p. cm. ISBN 978-953-51-0913-6 free online editions of InTech Books and Journals can be found at www.intechopen.com Contents Preface VII Chapter 1 Using Multiobjective Genetic Algorithm and Multicriteria Analysis for the Production Scheduling of a Brazilian Garment Company 1 Dalessandro Soares Vianna, Igor Carlos Pulini and Carlos Bazilio Martins Chapter 2 Grasp and Path Relinking to Solve the Problem of Selecting Efficient Work Teams 25 Fernando Sandoya and Ricardo Aceves Chapter 3 Meta-Heuristic Optimization Techniques and Its Applications in Robotics 53 Alejandra Cruz-Bernal Chapter 4 A Comparative Study on Meta Heuristic Algorithms for Solving Multilevel Lot-Sizing Problems 77 Ikou Kaku, Yiyong Xiao and Yi Han Chapter 5 A Two-Step Optimisation Method for Dynamic Weapon Target Assignment Problem 109 Cédric Leboucher, Hyo-Sang Shin, Patrick Siarry, Rachid Chelouah, Stéphane Le Ménec and Antonios Tsourdos Preface The last decade has witnessed a sharp increase in the dimensionality of different underlying optimization paradigms stemming from a variety of fields and scenarios. Examples abound not only in what relates to purely technological sectors, but also in other multiple disci‐ plines, ranging from bioinformatics to finance, economics, operational research, logistics, so‐ cial and food sciences, among many others. Indeed, almost every single aspect driving this increased dimensionality has grown exponentially as exemplified by the upsurge of com‐ munication terminals for the optimization of cellular network planning or the rising need for sequence alignment, analysis, and annotation in genomics. As a result, the computational complexity derived from solving TeAM YYeP G Digitally signed by TeAM YYePG DN: cn=TeAM YYePG, c=US, o=TeAM YYePG, ou=TeAM YYePG, email=yyepg@msn.com Reason: I attest to the accuracy and integrity of this document Date: 2005.04.27 16:01:23 +08'00' [...]... never go wrong Rather, I mean that there’s never a wrong time to invest if you choose the right strategy And that’s what I’m going to show you Get Started Now 7 You Must Believe It to See It Given the large rewards that most savvy real estate investors have achieved over the years, I’ve often wondered why most people fail to invest in real estate After much thought and talks with hundreds of would-be... previous Wiley titles Here you’ll find discussions about credit scoring, mortgages, seller financing, negotiation, foreclosures, bargain-hunting, appraisal, valuation, creating value, cash flow analysis, property management, and dozens of other topics In this book, you’ll gain a profit-generating introduction to the complete range of knowledge you’ll need to begin building wealth in real estate In other words,... taking positive action As to real estate investing, I urge you to reprogram your negative self-talk and limiting beliefs with mind-opening questions such as these: ◆ What are six ways I ◆ Where are the best can save more and spend less? neighborhoods to find bargain-priced prop- erties? might I persuade the sellers to accept owner financing? do I know with money that I could partner with? can I boost my credit... of them So, will you join the ranks of the naysayers? 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Starting late most assuredly beats never starting at all To know that most of these folks are now rushing into low-yielding... knowledge, time, and effort It’s certainly true.You can still get rich in real estate But you must learn how to analyze properties, neighborhoods, and financial risks and rewards And that’s exactly what my books will help you learn I wish you good luck and good fortune Gary W Eldred The BEGINNER’S ... divide into nominal GDP: $543.3 billion / 0.19 = $2,859.5 billion 4/9 Adjusting Nominal Values to Real Values Step Use the same formula to calculate the real GDP in 1965 Real GDP = Nominal GDP... $90 Then, 3/9 Adjusting Nominal Values to Real Values Coolshirt's real income = Nominal revenue Price = $90 $9 = 10 In other words, when we compute real measurements we are trying to get at actual... the GDP deflator are given in [link] and shown graphically in [link] 2/9 Adjusting Nominal Values to Real Values U.S GDP Deflator, 1960–2010 Much like nominal GDP, the GDP deflator has risen