Dr. Grami received his PhD in Electrical Engineering from the University of Toronto. He has worked for Nortel Networks, where he was involved in the research, design, and development of North America's first digital cellular wireless system.He later joined Telesat Canada, where he was the lead researcher and principal designer of Canada's Anik-F2 Ka-band system, the world's first broadband access satellite system. Dr. Grami is currently an associate professor in the Faculty of Engineering and Applied Science at the University of Ontario Institute of Technology (UOIT), where as a founding faculty member he has led the development of various programs, including the BEng, MEng, and PhD programs in ECE.
Introduction to Digital Communications explores the basic principles in the analysis and design of digital communication systems, including design objectives, constraints and trade-offs. After portraying the big picture and laying the background material, this book lucidly progresses to a comprehensive and detailed discussion of all critical elements and key functions in digital communications. - The first undergraduate-level textbook exclusively on digital communications, with a complete coverage of source and channel coding, modulation, and synchronization. - Discusses major aspects of communication networks and multiuser communications- Provides insightful descriptions and intuitive explanations of all complex concepts- Focuses on practical applications and illustrative examples. - A companion Web site includes solutions to end-of-chapter problems and computer exercises, lecture slides, and figures and tables from the text
Front Cover 1
Introduction to Digital Communications 4
Copyright 5
Dedication 6
Contents 8
Preface 14
Acknowledgements 16
Chapter 1: Introduction 18
1.1. Historical Review of Communications 18
1.2. Block Diagram of a Digital Communication System 22
1.3. Organization of the Book 25
References 27
Chapter 2: Fundamental Aspects of Digital Communications 28
Introduction 28
Contents 28
2.1. Why Digital? 29
2.1.1. Advantages of Digital 30
2.1.2. Disadvantages of Digital 31
2.2. Communications modalities 32
2.2.1. Text 32
2.2.2. Audio 33
2.2.3. Visual 34
2.3. Communication network models 35
2.3.1. Layered Architectures 36
2.3.2. OSI Model 36
2.3.3. TCP/IP Protocol Suite 39
2.4. Guided-Transmission Media 40
2.4.1. Twisted-Pair Cable 40
2.4.2. Coaxial Cable 42
2.4.3. Fiber-Optic Cable 42
2.5. Radio transmission 43
2.5.1. Advantages of Radio 43
2.5.2. Disadvantages of Radio 43
2.5.3. Radio Spectrum 44
2.5.4. Wave Propagation 45
2.6. Transmission impairments 48
2.6.1. Attenuation 48
2.6.2. Distortion 48
2.6.3. Interference 50
2.6.4. Noise 51
2.7. Modulation process 51
2.8. Fundamental limits in digital transmission 54
2.9. Digital communication design aspects 54
Summary and Sources 56
Chapter 3: Signals, Systems, and Spectral Analysis 58
Introduction 58
3.1. Basic operations on signals 59
3.1.1. Operations Performed on Dependent Variable 59
3.1.2. Operations Performed on Independent Variable 63
3.2. Classification of signals 66
3.2.1. Continuous-Value and Discrete-Value Signals 66
3.2.2. Continuous-Time and Discrete-Time Signals 66
3.2.3. Analog and Digital Signals 67
3.2.4. Deterministic and Random Signals 68
3.2.5. Real and Complex Signals 68
3.2.6. Periodic and Nonperiodic Signals 69
3.2.7. Even and Odd Signals 70
3.2.8. Energy and Power Signals 71
3.2.9. Causal and Noncausal Signals 73
3.2.10. Time-Limited and Band-Limited Signals 73
3.2.11. Baseband and Bandpass Signals 74
3.3. Classification of systems 74
3.3.1. Baseband and Passband Systems 75
3.3.2. Invertible and Noninvertible Systems 75
3.3.3. Lumped and Distributed Systems 75
3.3.4. Adaptive and Fixed Systems 76
3.3.5. Systems with or without Feedback 76
3.3.6. Systems with or without Memory 77
3.3.7. Systems with Single/Multiple Inputs and Single/Multiple Outputs 77
3.3.8. Passive and Active Systems 78
3.3.9. Causal and Noncausal Systems 78
3.3.10. Stable and Unstable Systems 78
3.3.11. Continuous-Time and Discrete-Time Systems 78
3.3.12. Power-Limited and Band-Limited Systems 78
3.3.13. Linear and Nonlinear Systems 79
3.3.14. Time-Invariant and Time-Varying Systems 80
3.3.15. Linear Time-Invariant (LTI) Systems 81
3.4. Sinsuoidal signals 82
3.4.1. Characteristics of Sinusoidal Signals 82
3.4.2. Benefits and Applications of Sinusoidal Signals 85
3.4.3. Relation between Sinusoidal and Complex Exponential Signals 86
3.5. Elementary signals 88
3.5.1. DC Signal 88
3.5.2. Unit Step Function 88
3.5.3. Exponential Signal 89
3.5.4. Sinc Function 89
3.5.5. Gaussian Pulse 90
3.5.6. Unit Ramp Function 90
3.5.7. Signum Function 91
3.5.8. Rectangular Pulse 92
3.5.9. Dirac Delta or Unit Impulse Function 93
3.5.10. Periodic Pulse and Impulse Trains 94
3.6. Fourier series 95
3.6.1. Orthogonal Functions 95
3.6.2. Dirichlets Conditions 96
3.6.3. Quadrature Fourier Series 97
3.6.4. Polar Fourier Series 100
3.6.5. Complex Exponential Fourier Series 101
3.6.6. Spectrum of Periodic Signals 101
3.6.7. Power of Periodic Signals 104
3.7. Fourier transform 105
3.7.1. Fourier Transform Pair 106
3.7.2. Fourier Spectra 107
3.7.3. Fourier Transform for Periodic Signals 111
3.7.4. Properties of Fourier Transform 114
3.7.5. Numerical Computation of Fourier Transform: Discrete Fourier Transform 130
3.8. Time and frequency relations 133
3.8.1. Bandwidth Definitions 133
3.8.2. Time-Bandwidth Product 135
3.9. Signal Transmission through systems 137
3.9.1. Signal Transmission through LTI Systems 137
3.9.2. Time Response and Convolution in LTI Systems 140
3.9.3. Frequency Response and Transfer Function in LTI Systems 141
3.9.4. Application of Periodic Signals to LTI Systems 143
3.9.5. Distortionless Transmission 144
3.9.6. Nonlinear Distortion 146
3.10. Communication filters 148
3.10.1. Ideal Filters 148
3.10.2. Filter Types 151
3.10.3. Filter Design 152
3.11. Spectral density and autocorrelation functions 153
3.11.1. Energy Spectral Density 154
3.11.2. Autocorrelation of Energy Signals 154
3.11.3. Power Spectral Density 155
3.11.4. Autocorrelation of Power Signals 156
3.12. Lowpass and bandpass signals 157
3.12.1. Lowpass Representation of Bandpass Signals 158
3.12.2. Quadrature Amplitude Modulation 158
3.12.3. Phase and Group Delay 159
Summary and Sources 161
Problems 162
Computer Exercises 166
Chapter 4: Probability, Random Variables, and Random Processes 168
Introduction 168
4.1. Probability 169
4.1.1. Basic Definitions 169
4.1.2. Axioms of Probability 170
4.1.3. Conditional Probability and Bayes Rule 171
4.2. Random variables 177
4.2.1. Single Random Variable 177
4.2.2. Important Single Random Variables 181
4.2.3. Expected Value 186
4.2.4. Conditional cdf and pdf of a Random Variable 188
4.2.5. Functions of a Single Random Variable 189
4.2.6. Chebyshev Inequality 191
4.2.7. Pair of Random Variables 192
4.2.8. Independent, Uncorrelated, and Orthogonal Random Variables 195
4.2.9. Jointly Gaussian Random Variables 198
4.2.10. Sum of Random Variables 198
4.3. Random processes 201
4.3.1. Basic Concepts 201
4.3.2. Statistical Averages 203
4.3.3. Stationary Processes 204
4.3.4. Ergodic Processes 207
4.3.5. Power Spectral Density 209
4.3.6. Response of Linear Time-Invariant Systems to Random Processes 212
4.3.7. Gaussian Random Process 214
4.3.8. Noise 216
4.3.9. Narrowband Bandpass Noise 218
4.3.10. Sampling Theorem of Random Signals 220
Summary and Sources 221
Problems 222
Computer Exercises 233
Chapter 5: Analog-to-Digital Conversion 234
Introduction 234
5.1. Sampling process 235
5.1.1. Sampling Theorem 236
5.1.2. Undersampling and Aliasing Effect 241
5.1.3. Natural Sampling and Flat-Top Sampling 245
5.1.4. Upsampling and Oversampling 249
5.1.5. Sampling of Bandpass Signals and Random Signals 250
5.2. Quantization process 253
5.2.1. Uniform Quantization 254
5.2.2. Nonuniform Quantization 257
5.2.3. Vector Quantization 261
5.3. Digital pulse modulation 263
5.3.1. Pulse-Code Modulation (PCM) 264
5.3.2. Differential PCM (DPCM) and Adaptive DPCM (ADPCM) 269
5.3.3. Delta Modulation (DM) and Adaptive DM (ADM) 271
5.4. Line codes 273
5.4.1. Line Coding Schemes and Selection Criteria 273
5.4.2. Power Spectral Density of Line Codes 275
Summary and Sources 277
Problems 278
Computer Exercises 281
Chapter 6: Baseband Digital Transmission 282
Introduction 282
6.1. Baseband binary PAM transmission system model 283
6.2. Intersymbol interference 285
6.2.1. Nyquist Criterion for Distortionless (Zero-ISI) Transmission 285
6.2.2. Raised-Cosine Pulse Spectrum 290
6.2.3. Eye Diagrams 290
6.3. Optimum system design for noise immunity 294
6.3.1. Bit Error Rate Derivation 295
6.3.2. Optimum Transmitting and Receiving Filters 296
6.3.3. Design Procedure and Example 297
6.4. Baseband M-ary signaling schemes 299
6.4.1. Bandwidth and Bit Rate 299
6.4.2. Power and Bit Error Rate 300
6.4.3. Binary vs. M-ary Signaling Schemes 302
6.5. Equalization 303
6.5.1. Viterbi Equalizers 303
6.5.2. Linear Equalizers 305
6.5.3. Decision-Feedback Equalizers 307
6.5.4. Adaptive Equalization 308
Summary and Sources 310
Problems 311
Computer Exercises 314
Chapter 7: Passband Digital Transmission 316
Introduction 316
7.1. Optimum receiver principles 317
7.1.1. System Model 317
7.1.2. Gram-Schmidt Orthogonalization Procedure 319
7.1.3. Geometric Representation and Interpretation of Signals 322
7.1.4. Receiver Implementation 323
7.1.5. Probability of Error 327
7.1.6. Nonwhite Noise and Noncoherent Detection 331
7.2. Binary digital modulation schemes 333
7.2.1. Binary Amplitude-Shift Keying 334
7.2.2. Binary Frequency-Shift Keying 336
7.2.3. Binary Phase-Shift Keying 339
7.2.4. Comparison of Binary Digital Modulation Schemes 343
7.3. Coherent quaternary signaling schemes 345
7.3.1. Quadrature Phase-Shift Keying 345
7.3.2. Offset Quadrature Phase-Shift Keying 350
7.3.3. Minimum-Shift Keying 350
7.4. M-ary coherent modulation techniques 354
7.4.1. M-ary Amplitude-Shift Keying 355
7.4.2. M-ary Phase-Shift Keying 357
7.4.3. M-ary Quadrature Amplitude Modulation 359
7.4.4. M-ary Frequency-Shift Keying 363
7.4.5. Comparison of M-ary Modulation Schemes 365
7.5. Orthogonal Frequency-Division Multiplexing 367
Summary and Sources 369
Problems 370
Computer Exercises 372
Chapter 8: Synchronization 374
Introduction 374
8.1. Synchronization levels 375
8.2. Scrambling 376
8.2.1. Pseudorandom Scrambler 377
8.2.2. Self-Synchronizing Scrambler 379
8.3. Phase-Locked Loop (PLL) 380
8.3.1. Basic Operation 381
8.3.2. Linear Model of PLL 383
8.4. Carrier Recovery 385
8.4.1. The Mth-Power Loop 385
8.4.2. The Costas Loop 386
8.5. Symbol Synchronization 387
8.5.1. Nonlinear-Filter Synchronizer 388
8.5.2. Early-Late Gate Synchronizer 389
Summary and Sources 391
Problems 391
Computer Exercises 392
Chapter 9: Information Theory 394
Introduction 394
9.1. Measure of information 395
9.1.1. Information Content 395
9.1.2. Average Information Content 397
9.1.3. Extended DMS 399
9.2. Classification of source codes 401
9.2.1. Block Codes 401
9.2.2. Fixed-Length Codes 401
9.2.3. Variable-Length Codes 402
9.2.4. Distinct Codes 402
9.2.5. Prefix-Free (Instantaneous) Codes 402
9.2.6. Uniquely Decodable Codes 402
9.2.7. Kraft Inequality 403
9.2.8. Extension Codes 404
9.3. Source Coding theorem 405
9.4. Lossless data compression 408
9.4.1. Huffman Source Coding Algorithm 408
9.4.2. Lempel-Ziv Source Coding Algorithm 412
9.5. Discrete Memoryless channels 414
9.5.1. Channel Transition Probabilities 414
9.5.2. Mutual Information 415
9.5.3. Capacity of Discrete Memory Channel 416
9.6. Channel coding theorem 417
9.7. Gaussian Channel Capacity Theorem 418
Summary and Sources 421
Problems 422
Computer Exercises 425
Chapter 10: Error-Control Coding 426
Introduction 426
10.1. Errors 427
10.1.1. Types of Errors 427
10.1.2. Methods of Controlling Errors 428
10.1.3. Classes of Codes 429
10.1.4. Decoding Methods 430
10.2. Error-detection methods 431
10.2.1. Parity-Check Codes 431
10.2.2. Checksum 434
10.2.3. Cyclic Redundancy Check 435
10.3. Automatic Repeat Request (ARQ) 438
10.3.1. Stop-and-Wait, Go-Back-N, and Selective-Repeat ARQ Techniques 439
10.3.2. Performance of ARQ Systems 441
10.4. Block codes 443
10.4.1. Description and Capabilities of Linear Block Codes 443
10.4.2. Syndrome-Based Decoding 447
10.4.3. Well-Known Codes 450
10.5. Convolutional codes 452
10.5.1. Representations of Convolutional Codes 453
10.5.2. Maximum-Likelihood Decoding: The Viterbi Algorithm 457
10.5.3. Trellis-Coded Modulation 459
10.6. Compound codes 461
10.6.1. Interleavering 462
10.6.2. Simple Combining Codes 465
10.6.3. Turbo Codes 467
10.6.4. Low-Density Parity-Check Codes 470
Summary and Sources 470
Problems 471
Computer Exercises 472
Chapter 11: Communication Networks 474
Introduction 474
11.1. Multiplexing 475
11.1.1. Frequency-Division Multiplexing 475
11.1.2. Time-Division Multiplexing 477
11.1.3. Wavelength-Division Multiplexing 477
11.2. Duplexing 478
11.2.1. Frequency-Division Duplexing 479
11.2.2. Time-Division Duplexing 481
11.3. Multiple Access 481
11.3.1. Frequency-Division Multiple Access 482
11.3.2. Time-Division Multiple Access 482
11.3.3. Code-Division Multiple Access 484
11.4. Random access 485
11.4.1. ALOHA 485
11.4.2. CSMA 488
11.5. Controlled Access 490
11.5.1. Reservation 490
11.5.2. Polling 491
11.6. Wired Communication Networks 491
11.6.1. Circuit-Switched and Packet-Switched Networks 492
11.6.2. Topology 493
11.6.3. Routing and Flow Control 496
11.6.4. Local Area Networks 497
11.6.5. Telephone and Cable Networks 499
11.7. Network Security and Cryptography 502
11.7.1. Private-Key Cryptography 503
11.7.2. Public-Key Cryptography 504
11.7.3. Digital Signatures 505
Summary and Sources 507
Problems 508
Chapter 12: Wireless Communications 510
Introduction 510
12.1. Radio-link analysis 511
12.1.1. Sources of Interference, Loss, and Noise 511
12.1.2. Received Signal Power and Path Loss 512
12.1.3. Noise Temperature and Receive Figure of Merit 513
12.1.4. Link Margin and Link Threshold 514
12.2. Frequency reuse 515
12.2.1. Dual Polarization 516
12.2.2. Spatial Separation 517
12.3. Mobile-radio propagation characteristics 521
12.3.1. Radio-Propagation Mechanisms 521
12.3.2. Doppler Effect 523
12.3.3. Delay Spread and Coherent Bandwidth 524
12.3.4. Doppler Spread and Coherence Time 525
12.3.5. Large-Scale Fading and Small-Scale Fading 525
12.3.6. Fast Fading and Slow Fading 526
12.3.7. Flat Fading and Frequency-Selective Fading 527
12.4. Diversity 528
12.4.1. Time Diversity 529
12.4.2. Space Diversity 530
12.4.3. Site Diversity 530
12.4.4. Frequency Diversity 530
12.4.5. Polarization Diversity 531
12.4.6. Angle Diversity 531
12.4.7. Path Diversity 531
12.5. Diversity-combining methods 532
12.5.1. Selection Combining 532
12.5.2. Maximal-Ratio Combining 533
12.5.3. Equal-Gain Combining 533
12.6. Emerging wireless communication systems 534
12.6.1. Evolution of Wireless Communication Systems 534
12.6.2. 4G Systems 535
12.6.3. TV White Spaces 540
Summary and Sources 542
Problems 543
Appendix: Analog Continuous-Wave Modulation 546
Introduction 546
A.1. Analog Continuous-Wave (CW) Modulation 547
A.2. Amplitude moDUlation 549
A.2.1. Conventional Amplitude Modulation 550
A.2.2. Double-Sideband Suppressed-Carrier Amplitude Modulation 556
A.2.3. Single-Sideband Amplitude Modulation 559
A.2.4. Vestigial-Sideband Amplitude Modulation 560
A.3. Frequency modUlation 567
A.3.1. Representation of FM Signals 567
A.3.2. Spectral Analysis of FM Signals 568
A.3.3. FM Modulation and Demodulation 571
A.4. Amplitude Nonlinearity in Analog CW Modulation 573
A.4.1. Effect of Amplitude Nonlinearity on AM Systems 573
A.4.2. Effect of Amplitude Nonlinearity on FM Systems 574
A.5. Noise in analog CW modulation 575
A.5.1. Effect of Noise on AM Systems 576
A.5.2. Effect of Noise on FM Systems 577
A.6. Commercial radio broadcasting 580
A.6.1. AM Radio Broadcasting and Reception 580
A.6.2. FM Radio Broadcasting and Reception 582
A.7. Comparison of Analog CW Modulation Schemes 584
Summary and Sources 585
List of Acronyms and Abbreviations 590
Index 596
Fundamental Aspects of Digital Communications
Abstract
This chapter briefly provides a descriptive overview of major aspects of digital communications with a view to set the stage for what will be covered in the rest of the book. A quantitative discussion and detailed analysis of critical elements of digital communication systems will be provided in the following chapters. To provide a fundamental understanding of digital communication system analysis and design, this chapter begins with the rationale behind digital, vis-à-vis analog. The focus then turns toward network models, transmission media and impairments, and radio transmission and spectrum. Following a brief discussion on the fundamental limits in digital transmission, an array of inter-related, inter-dependent design objectives and a host of interacting and conflicting design constraints are identified.
Keywords
Digital
communication modality
OSI model
TCP/IP model;twisted-pair
coaxial cable
fiber-optic cable
wave propagation mode
radio spectrum
frequency band
transmission impairment
modulation process
design objective
design constraint
Contents
Introduction 11
2.1 Why Digital? 12
2.2 Communications Modalities 15
2.3 Communication Network Models 18
2.4 Guided-Transmission Media 23
2.5 Radio Transmission 26
2.6 Transmission Impairments 31
2.7 Modulation Process 34
2.8 Fundamental Limits in Digital Transmission 37
Introduction
In today’s world, communications are essential and pervasive, as the age of communications with anyone, anytime, anywhere has arrived. The theme is multimedia—the confluence of voice, data, image, music, text, graphics, and video warranting simultaneous transmission in an integrated fashion. With the push of advancing digital technology and the pull of public demand for an array of innovative applications, it is highly anticipated that every aspect of digital communications will continue to broaden so as to usher in even more achievements. The emerging trend is toward low-cost, high-speed, high-performance, utterly-secure, highly-personalized, context-aware, location-sensitive, and time-critical multimedia applications. After studying this chapter on the fundamental aspects of digital communications and understanding all relevant concepts, students should be able to do the following:
1. State the numerous merits of digital and its dominance in communications.
2. Know the few drawbacks of digital and how they can be mitigated.
3. Understand how text can be represented.
4. Expand on the audio characteristics and the impact of digitization on speech and music.
5. Explain the attributes of image and video and the impact of compression on them.
6. Identify how computers form packets to send them over communication networks.
7. Distinguish between the various characteristics associated with wired transmission media.
8. Highlight the benefits and shortcomings associated with radio communications.
9. Assess various modes of radio wave propagation.
10. Define the modulation process.
11. Identify the principal reasons signals may need to be modulated.
12. Describe signal attenuation.
13. Differentiate among different types of distortions along with their possible remedies.
14. Discuss various sources of interference and how to mitigate them.
15. Summarize various sources of noise.
16. Grasp the limiting factors of a band-limited Gaussian channel.
17. Appreciate the relationship among power, bandwidth, and capacity.
18. Outline digital communication design objectives.
19. List digital communication design constraints.
20. Connect the fundamental aspects of digital communications.
2.1 Why Digital?
The telegraph, invented in the mid-nineteenth century, was the forerunner of digital communications. However, it is now that we can emphatically say digital is the pervasive technology of the twenty-first century and beyond, as the first generation of cellular phones in the late seventies was the last major analog communication invention. During the past three decades, communication networks, systems, and devices have all moved toward digital. The primary examples are wireless networks, Internet, MP3 players, smartphones, HDTV, GPS, and satellite TV and radio. Digital communication technology will continue to bring about intelligent infrastructures and sophisticated end-user devices, through which a host of applications in entertainment (e.g., wireless video on demand), education (e.g., online interactive multimedia courses), information (e.g., 3-D video streaming), and business (e.g., mobile commerce) will be provided. The burgeoning field of digital communications will thus continue to affect almost all aspects of our contemporary life.
A basic definition of digital is the transmission of a message using binary digits (bits) or symbols from a finite alphabet during a finite time interval (bit or symbol duration). A bit or symbol occurring in each interval is mapped onto a continuous-time waveform that is then sent across the channel. Over any finite interval, the continuous-time waveform at the channel output belongs to a finite set of possible waveforms. This is in contrast to analog communications, where the output can assume any possible waveform. Digital can bring about many significant benefits, of course, at the expense of few shortcomings, for there is no free lunch in digital communications.
2.1.1 Advantages of Digital
Design efficiency: Digital is inherently more efficient than analog in exchanging power for bandwidth, the two premium resources in communications. Since an essentially unlimited range of signal conditioning and processing options are available to the designer, effective trade-offs among power, bandwidth, performance, and complexity can be more readily accommodated. For any required performance, there is a three-way trade-off among power, bandwidth, and complexity (i.e., an increase in one means the other two will be reduced).
Versatile hardware: The processing power of digital integrated circuits continues to approximately double every 18 months to 2 years. These programmable processors easily allow the implementation of improved designs or changed requirements. Digital circuits are generally less sensitive to physical effects, such as vibration, aging components, and external temperature. They also allow a greater dynamic range (the difference between the largest and the smallest signal values). Processing is now less costly than precious bandwidth and power resources. This in turn allows considerable flexibility in designing communication systems.
New and enhanced services: In today’s widely distributed way of life, Internet services, such as web browsing, e-mailing, texting, e-commerce, streaming and interactive multimedia services, have all become feasible and some even indispensable. It is also easier to integrate different services, with various modalities, into the same transmission scheme or to enhance services through transmission of some additional information, such as playing music or receiving a phone call with all relevant details.
Control of quality: A desired distortion level can be initially set and then kept nearly fixed at that value at every step (link) of a digital communication path. This reconstruction of the digital signal is done by appropriately-spaced regenerative repeaters, which do not allow accumulation of noise and interference. On the other hand, once the analog signal is distorted, the distortion cannot be removed and a repeater in an analog system (i.e., an amplifier) regenerates the distortion together with the signal. In a way, in an analog system, the noises add, whereas in a digital system, the bit error rates add. In other words, with many regenerative repeaters along the path, the impact in an analog system is a reduction of many decibels (dBs) in the signal-to-noise ratio (SNR), whereas the effect in a digital system is a reduction of only a few dBs in the SNR.
Improved security: Digital encryption,...
| Erscheint lt. Verlag | 25.2.2015 |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik | |
| Technik ► Elektrotechnik / Energietechnik | |
| Technik ► Nachrichtentechnik | |
| ISBN-10 | 0-12-407658-0 / 0124076580 |
| ISBN-13 | 978-0-12-407658-7 / 9780124076587 |
| Haben Sie eine Frage zum Produkt? |
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