Signals and Systems using MATLAB (eBook)

Luis F. Chaparro (Autor)

eBook Download: PDF | EPUB

2010 | 1. Auflage
768 Seiten
Elsevier Science (Verlag)
978-0-08-087933-8 (ISBN)

Infos

This new textbook in signals and systems provides a pedagogically rich approach to what can commonly be a mathematically dry subject. With features like historical notes, highlighted common mistakes, and applications in controls, communications, and signal processing, Chaparro helps students appreciate the usefulness of the techniques described in the book. Each chapter contains a section with MatLab applications. - Pedagogically rich introduction to signals and systems using historical notes, pointing out 'common mistakes', and relating concepts to realistic examples throughout to motivate learning the material - Introduces both continuous and discrete systems early, then studies each (separately) in more depth later - Extensive set of worked examples and homework assignments, with applications to controls, communications, and signal processing throughout - Provides review of all the background math necessary to study the subject - MatLab applications in every chapter

Dr. Chaparro's research interests include statistical signal processing, time-frequency analysis, nonlinear image processing and multidimensional system theory. He is a senior Member of IEEE, Associate Editor of the Journal of the Franklin Institute, past Associate Editor of the IEEE Transaction on Signal Processing and member of the IEEE Technical Committee on Statistical Signal and Array Processing.

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This new textbook in signals and systems provides a pedagogically rich approach to what can commonly be a mathematically dry subject. With features like historical notes, highlighted common mistakes, and applications in controls, communications, and signal processing, Chaparro helps students appreciate the usefulness of the techniques described in the book. Each chapter contains a section with MatLab applications. - Pedagogically rich introduction to signals and systems using historical notes, pointing out "e;common mistakes"e;, and relating concepts to realistic examples throughout to motivate learning the material- Introduces both continuous and discrete systems early, then studies each (separately) in more depth later- Extensive set of worked examples and homework assignments, with applications to controls, communications, and signal processing throughout- Provides review of all the background math necessary to study the subject- MatLab applications in every chapter

Inhalt

Front cover 1
Signals and Systems Using MATLAB® 2
Copyright page 3
Dedication 4
Table of contents 5
Preface 12
Acknowledgments 17
Part 1: Introduction 18
Chapter 0. From the Ground Up! 20
0.1 Signals and Systems and Digital Technologies 20
0.2 Examples of Signal Processing Applications 22
0.3 Analog or Discrete? 26
0.4 Complex or Real? 37
0.5 Soft Introduction to MATLAB 46
Problems 70
Part 2: Theory and Application of Continuous-Time Signals and Systems 80
Chapter 1. Continuous-Time Signals 82
1.1 Introduction 82
1.2 Classification of Time-Dependent Signals 83
1.3 Continuous-Time Signals 84
1.4 Representation Using Basic Signals 102
1.5 What Have We Accomplished? Where Do We Go from Here? 123
Problems 125
Chapter 2. Continuous-Time Systems 134
2.1 Introduction 134
2.2 System Concept 135
2.3 LTI Continuous-Time Systems 136
2.4 What Have We Accomplished? Where Do We Go from Here? 173
Problems 174
Chapter 3. The Laplace Transform 182
3.1 Introduction 182
3.2 The Two-Sided Laplace Transform 183
3.3 The One-Sided Laplace Transform 193
3.4 Inverse Laplace Transform 214
3.5 Analysis of LTI Systems 231
3.6 What Have We Accomplished? Where Do We Go from Here? 243
Problems 243
Chapter 4. Frequency Analysis: The Fourier Series 254
4.1 Introduction 254
4.2 Eigenfunctions Revisited 255
4.3 Complex Exponential Fourier Series 262
4.4 Line Spectra 265
4.5 Trigonometric Fourier Series 268
4.6 Fourier Coefficients from Laplace 272
4.7 Convergence of the Fourier Series 282
4.8 Time and Frequency Shifting 287
4.9 Response of LTI Systems to Periodic Signals 290
4.10 Other Properties of the Fourier Series 296
4.11 What Have We Accomplished? Where Do We Go from Here? 306
Problems 307
Chapter 5. Frequency Analysis: The Fourier Transform 316
5.1 Introduction 316
5.2 From the Fourier Series to the Fourier Transform 317
5.3 Existence of the Fourier Transform 319
5.4 Fourier Transforms from the Laplace Transform 319
5.5 Linearity, Inverse Proportionality, and Duality 321
5.6 Spectral Representation 330
5.7 Convolution and Filtering 344
5.8 Additional Properties 361
5.9 What have We Accomplished? What is next? 367
Problems 367
Chapter 6. Application to Control and Communications 376
6.1 Introduction 376
6.2 System Connections and Block Diagrams 377
6.3 Application to Classic Control 380
6.4 Application to Communications 394
6.5 Analog Filtering 407
6.6 What Have We Accomplished? What is next? 426
Problems 426
Part 3: Theory and Application of Discrete-Time Signals and Systems 434
Chapter 7. Sampling Theory 436
7.1 Introduction 436
7.2 Uniform Sampling 437
7.3 The Nyquist-Shannon Sampling Theorem 454
7.4 Practical Aspects of Sampling 456
7.5 What Have We Accomplished? Where Do We Go from Here? 463
Problems 464
Chapter 8. Discrete-Time Signals and Systems 468
8.1 Introduction 468
8.2 Discrete-Time Signals 469
8.3 Discrete-Time Systems 495
8.4 What Have We Accomplished? Where Do We Go from Here? 519
Problems 519
Chapter 9. The Z-Transform 528
9.1 Introduction 528
9.2 Laplace Transform of Sampled Signals 529
9.3 Two-Sided Z-Transform 532
9.4 One-Sided Z-Transform 538
9.5 One-Sided Z-Transform Inverse 559
9.6 What Have We Accomplished? Where Do We Go from Here? 581
Problems 581
Chapter 10. Fourier Analysis of Discrete-Time Signals and Systems 588
10.1 Introduction 588
10.2 Discrete-Time Fourier Transform 589
10.3 Fourier Series of Discrete-Time Periodic Signals 613
10.4 Discrete Fourier Transform 631
10.5 What Have We Accomplished? Where Do We Go from Here? 645
Problems 646
Chapter 11. Introduction to the Design of Discrete Filters 656
11.1 Introduction 656
11.2 Frequency-Selective Discrete Filters 658
11.3 Filter Specifications 665
11.4 IIR Filter Design 670
11.5 FIR Filter Design 696
11.6 Realization of Discrete Filters 706
11.7 What Have We Accomplished? Where Do We Go from Here? 718
Problems 718
Chapter 12. Applications of Discrete-Time Signals and Systems 726
12.1 Introduction 726
12.2 Application to Digital Signal Processing 727
12.3 Application to Sampled-Data and Digital Control Systems 739
12.4 Application to Digital Communications 746
12.5 What Have We Accomplished? Where Do We Go from Here? 758
Appendix. Useful Formulas 760
Bibliography 763
Index 766

Textauszug

Chapter 0

From the Ground Up!

In theory there is no difference between theory and practice. In practice there is.

Lawrence “Yogi” Berra, 1925 New York Yankees baseball player

This chapter provides an overview of the material in the book and highlights the mathematical background needed to understand the analysis of signals and systems. We consider a signal a function of time (or space if it is an image, or of time and space if it is a video signal), just like the voltages or currents encountered in circuits. A system is any device described by a mathematical model, just like the differential equations obtained for a circuit composed of resistors, capacitors, and inductors.

By means of practical applications, we illustrate in this chapter the importance of the theory of signals and systems and then proceed to connect some of the concepts of integro-differential Calculus with more concrete mathematics (from the computational point of view, i.e., using computers). A brief review of complex variables and their connection with the dynamics of systems follows. We end this chapter with a soft introduction to MATLAB, a widely used high-level computational tool for analysis and design.

Significantly, we have called this Chapter 0, because it is the ground floor for the rest of the material in the book. Not everything in this chapter has to be understood in a first reading, but we hope that as you go through the rest of the chapters in the book you will get to appreciate that the material in this chapter is the foundation of the book, and as such you should revisit it as often as needed.

0.1 Signals and Systems and Digital Technologies

In our modern world, signals of all kinds emanate from different types of devices—radios and TVs, cell phones, global positioning systems (GPSs), radars, and sonars. These systems allow us to communicate messages, to control processes, and to sense or measure signals. In the last 60 years, with the advent of the transistor, the digital computer, and the theoretical fundamentals of digital signal processing, the trend has been toward digital representation and processing of data, most of which are in analog form. Such a trend highlights the importance of learning how to represent signals in analog as well as in digital forms and how to model and design systems capable of dealing with different types of signals.

1948

The year 1948 is considered the birth year of technologies and theories responsible for the spectacular advances in communications, control, and biomedical engineering since then. In June 1948, Bell Telephone Laboratories announced the invention of the transistor. Later that month, a prototype computer built at Manchester University in the United Kingdom became the first operational stored-program computer. Also in that year, many fundamental theoretical results were published: Claude Shannon’s mathematical theory of communications, Richard W. Hamming’s theory on error-correcting codes, and Norbert Wiener’s Cybernetics comparing biological systems with communication and control systems [51].

Digital signal processing advances have gone hand-in-hand with progress in electronics and computers. In 1965, Gordon Moore, one of the founders of Intel, envisioned that the number of transistors on a chip would double about every two years [35]. Intel, the largest chip manufacturer in the world, has kept that pace for 40 years. But at the same time, the speed of the central processing unit (CPU) chips in desktop personal computers has dramatically increased. Consider the well-known Pentium group of chips (the Pentium Pro and the Pentium I to IV) introduced in the 1990s [34]. Figure 0.1 shows the range of speeds of these chips at the time of their introduction into the market, as well as the number of transistors on each of these chips. In five years, 1995 to 2000, the speed increased by a factor of 10 while the number of transistors went from 5.5 million to 42 million.

Figure 0.1 The Intel Pentium CPU chips. (a) Range of CPU speeds in MHz for the Pentium Pro (1995), Pentium II (1997), Pentium III (1999), and Pentium IV (2000). (b) Number of transistors (in millions) on each of the above chips. (Pentium data taken from [34].)

Advances in digital electronics and in computer engineering in the past 60 years have permitted the proliferation of digital technologies. Digital hardware and software process signals from cell phones, high-definition television (HDTV) receivers, radars, and sonars. The use of digital signal processors (DSPs) and more recently of field-programmable gate arrays (FPGAs) have been replacing the use of application-specific integrated circuits (ASICs) in industrial, medical, and military applications.

It is clear that digital technologies are here to stay. Today, digital transmission of voice, data, and video is common, and so is computer control. The abundance of algorithms for processing signals, and the pervasive presence of DSPs and FPGAs in thousands of applications make digital signal processing theory a necessary tool not only for engineers but for anybody who would be dealing with digital data; soon, that will be everybody! This book serves as an introduction to the theory of signals and systems—a necessary first step in the road toward understanding digital signal processing.

DSPs and FPGAs

A digital signal processor (DSP) is an optimized microprocessor used in real-time signal processing applications [67]. DSPs are typically embedded in larger systems (e.g., a desktop computer) handling general-purpose tasks. A DSP system typically consists of a processor, memory, analog-to-digital converters (ADCs), and digital-to-analog converters (DACs). The main difference with typical microprocessors is they are faster. A field-programmable gate array (FPGA) [77] is a semiconductor device containing programmable logic blocks that can be programmed to perform certain functions, and programmable interconnects. Although FPGAs are slower than their application-specific integrated circuits (ASICs) counterparts and use more power, their advantages include a shorter time to design and the ability to be reprogrammed.

0.2 Examples of Signal Processing Applications

The theory of signals and systems connects directly, among others, with communications, control, and biomedical engineering, and indirectly with mathematics and computer engineering. With the availability of digital technologies for processing signals, it is tempting to believe there is no need to understand their connection with analog technologies. It is precisely the opposite is illustrated by considering the following three interesting applications: the compact-disc (CD) player, software-defined radio and cognitive radio, and computer-controlled systems.

0.2.1 Compact-Disc Player

Compact discs [9] were first produced in Germany in 1982. Recorded voltage variations over time due to an acoustic sound is called an analog signal given its similarity with the differences in air pressure generated by the sound waves over time. Audio CDs and CD players illustrate best the conversion of a binary signal—unintelligible—into an intelligible analog signal. Moreover, the player is a very interesting control system.

To store an analog audio signal (e.g., voice or music) on a CD the signal must be first sampled and converted into a sequence of binary digits—a digital signal—by an ADC and then especially encoded to compress the information and to avoid errors when playing the CD. In the manufacturing of a CD, pits and bumps corresponding to the ones and zeros from the quantization and encoding processes are impressed on the surface of the disc. Such pits and bumps will be detected by the CD player and converted back into an analog signal that approximates the original signal when the CD is played. The transformation into an analog signal uses a DAC.

As we will see in Chapter 7, an audio signal is sampled at a rate of about 44,000 samples/second (sec) (corresponding to a maximum frequency around 22 KHz for a typical audio signal) and each of these samples is represented by a certain number of bits (typically 8 bits/sample). The need for stereo sound requires that two channels be recorded. Overall, the number of bits representing the signal is very large and needs to be compressed and especially encoded. The resulting data, in the form of pits and bumps impressed on the CD surface, are put into a spiral track that goes from the inside to the outside of the disc.

Besides the binary-to-analog conversion, the CD player exemplifies a very interesting control system (see Figure 0.2). Indeed, the player must: (1) rotate the disc at different speeds depending on the location of the track within the CD being read, (2) focus a laser and a lens system to read the pits and bumps on the disc, and (3) move the laser to follow the track being read. To understand the exactness required, consider that the width of the track and the high of the bumps is typically less than a micrometer (10−6 meters or 3.937 × 10−5 inches) and a nanometer (10−9 meters or 3.937 × 10−8 inches), respectively.

Figure 0.2 When playing a CD, the CD player follows the tracks in the disc, focusing a laser on them, as the CD is spun. The laser shines a light that is reflected by the pits and bumps put on the surface of the disc and corresponding to the coded digital signal from an acoustic signal. A sensor detects the reflected...

Produkt-Details

• Erscheint lt. Verlag: 10.11.2010
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Mathematik / Informatik ► Informatik ► Datenbanken
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Nachrichtentechnik
• ISBN-10: 0-08-087933-0 / 0080879330
• ISBN-13: 978-0-08-087933-8 / 9780080879338