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E-raamat: Modulation Theory [Taylor & Francis e-raamat]

(Federal University of Bahia (UFBA), Brazil)
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  • Taylor & Francis e-raamat
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In recent years, a considerable amount of effort has been devoted, both in industry and academia, towards the design, performance analysis and evaluation of modulation schemes to be used in wireless and optical networks and towards the development of the next and future generations of mobile cellular communication systems. Modulation Theory is intended to serve as a complementary textbook for courses dealing with Modulation Theory or Communication Systems, but also as a professional book, for engineers who need to update their knowledge in the communications area.

The modulation aspects presented in the book use modern concepts of stochastic processes, such as autocorrelation and power spectrum density, which are novel for undergraduate texts or professional books, and provides a general approach for the theory, with real life results, applied to professional design.

This text is suitable for the undergraduate as well as the initial graduate levels of Electrical Engineering courses, and is useful for the professional who wants to review or get acquainted with the a modern exposition of the modulation theory.

The book covers signal representations for most known waveforms and Fourier analysis and presents an introduction to Fourier transform and signal spectrum (including the concepts of convolution, autocorrelation and power spectral density) for deterministic signals. It introduces the concepts of probability, random variables and stochastic processes (including autocorrelation, cross-correlation, power spectral and cross-spectral densities) for random signals and their applications to the analysis of linear systems. This chapter also includes the response of specific non-linear systems, such as power amplifiers.

The book presents amplitude modulation with random signals--including analog and digital signals--and discusses performance evaluation methods, presents quadrature amplitude modulation using random signals. Several modulation schemes are discussed, including SSB, QAM, ISB, C-QUAM, QPSK and MSK. Their autocorrelation and power spectrum densities are computed. A thorough discussion on angle modulation with random modulating signals, along with frequency and phase modulation, and orthogonal frequency division multiplexing is provided. Their power spectrum densities are computed using the Wiener-Khintchin theorem.
Preface xiii
List of Figures xv
1 Theory of Signals and Linear Systems 1(38)
1.1 Introduction
1(1)
1.2 Signal Analysis
1(1)
1.2.1 Linearity
1(1)
1.2.2 The Convolution Theorem
2(1)
1.3 Some Important Functions
2(8)
1.3.1 The Constant Function
2(1)
1.3.2 The Sine and the Cosine Functions
2(1)
1.3.3 The Heaviside Step Function
3(1)
1.3.4 The Ramp Function
4(2)
1.3.5 The Gate Function
6(1)
1.3.6 Impulse Function or Dirac's Delta Function
7(2)
1.3.7 The Sampling Function
9(1)
1.3.8 Even and Odd Functions
9(1)
1.3.9 Some Elementary Properties of Functions
9(1)
1.4 Basic Fourier Analysis
10(7)
1.4.1 The Trigonometric Fourier Series
12(3)
1.4.2 The Compact Fourier Series
15(1)
1.4.3 The Exponential Fourier Series
15(2)
1.5 Fourier Transform
17(6)
1.5.1 Bilateral Exponential Signal
19(1)
1.5.2 Transform of the Gate Function
19(1)
1.5.3 Fourier Transform of the Impulse Function
20(1)
1.5.4 Transform of the Constant Function
21(1)
1.5.5 Fourier Transform of the Sine and Cosine Functions
22(1)
1.5.6 Fourier Transform of the Complex Exponential
23(1)
1.5.7 Fourier Transform of a Periodic Function
23(1)
1.6 Some Properties of the Fourier Transform
23(6)
1.6.1 Linearity of the Fourier Transform
23(1)
1.6.2 Scaling Property
24(1)
1.6.3 Symmetry of the Fourier Transform
25(1)
1.6.4 Time Domain Shift
26(1)
1.6.5 Frequency Domain Shift
26(1)
1.6.6 Differentiation in the Time Domain
26(1)
1.6.7 Integration in the Time Domain
27(1)
1.6.8 The Convolution Theorem in the Time Domain
28(1)
1.6.9 The Convolution Theorem in the Frequency Domain
29(1)
1.7 The Sampling Theorem
29(4)
1.8 Parseval's Theorem
33(1)
1.9 Average, Power, and Autocorrelation
33(6)
1.9.1 Time Autocorrelation of Signals
34(5)
2 Random Signals and Noise 39(60)
2.1 The Theory of Sets, Functions, and Measure
39(6)
2.1.1 Set Theory
40(1)
2.1.2 Operations on Sets
40(2)
2.1.3 Families of Sets
42(1)
2.1.4 Indexing Sets
42(1)
2.1.5 Algebra of Sets
42(2)
2.1.6 Borel Algebra
44(1)
2.2 Probability Theory
45(2)
2.2.1 Axiomatic Approach to Probability
45(1)
2.2.2 Bayes' Rule
46(1)
2.3 Random Variables
47(6)
2.3.1 Mean Value of a Random Variable
48(1)
2.3.2 Moments of a Random Variable
48(1)
2.3.3 The Variance of a Random Variable
48(1)
2.3.4 The Characteristic Function of a Random Variable
49(1)
2.3.5 Some Important Random Variables
49(2)
2.3.6 Joint Random Variables
51(2)
2.4 Stochastic Processes
53(21)
2.4.1 The Autocorrelation Function
53(1)
2.4.2 Stationarity
54(3)
2.4.3 Wide Sense Stationarity
57(1)
2.4.4 Ergodic Signals
58(1)
2.4.5 Properties of the Autocorrelation
58(5)
2.4.6 The Power Spectral Density
63(6)
2.4.7 Properties of the Power Spectral Density
69(5)
2.5 Linear Systems
74(8)
2.5.1 Expected Value of the Output Signal
75(1)
2.5.2 The Response of Linear Systems to Random Signals
75(5)
2.5.3 Phase Information
80(2)
2.6 Analysis of a Digital Signal
82(8)
2.6.1 Autocorrelation of a Digital Signal
83(2)
2.6.2 Power Spectral Density for the Digital Signal
85(4)
2.6.3 The Digital Signal Bandwidth
89(1)
2.7 Non-Linear Systems
90(9)
2.7.1 The Two-Level Quantizer
90(1)
2.7.2 Quantization Noise Spectrum for a Two-level Quantizer
90(3)
2.7.3 Response of a Squarer Circuit
93(1)
2.7.4 Response of a Non-Linear Amplifier
94(1)
2.7.5 Response of an Ideal Diode
95(4)
3 Amplitude Modulation Theory 99(22)
3.1 Introduction
99(1)
3.2 Amplitude Modulation
100(3)
3.3 Amplitude Modulation by Random Signals
103(4)
3.3.1 Power of an AM Carrier
105(1)
3.3.2 Power Spectral Density
105(2)
3.4 Amplitude Modulators
107(5)
3.4.1 Quadratic Modulator
107(2)
3.4.2 Synchronous Modulator
109(1)
3.4.3 Digital AM Signal
110(1)
3.4.4 AM Transmitter
111(1)
3.5 Suppressed Carrier Amplitude Modulation
112(1)
3.6 Spectrum of the AM-SC Signal
112(3)
3.6.1 Power Spectral Density
113(1)
3.6.2 The AM-SC Modulator
113(2)
3.7 AM-VSB Modulation
115(1)
3.8 Amplitude Demodulation
116(2)
3.9 Noise Performance of Amplitude Modulation
118(3)
4 Quadrature Amplitude Modulation Theory 121(22)
4.1 Quadrature Modulation with Random Signals
121(3)
4.2 Single Sideband Modulation
124(7)
4.2.1 Hilbert Transform
124(1)
4.2.2 Fourier Transform of 1/πt
125(1)
4.2.3 Properties of the Hilbert Transform
126(1)
4.2.4 Producing the SSB Signal
126(2)
4.2.5 Lower Sideband SSB with Random Signal
128(3)
4.3 ISB Modulation
131(2)
4.4 AM-Stereo
133(1)
4.5 Quadrature Amplitude Demodulation
134(1)
4.6 Performance Evaluation of SSB
135(1)
4.7 Digital Quadrature Modulation
136(7)
5 Angle Modulation Theory 143(24)
5.1 Introduction
143(1)
5.2 Angle Modulation with Stochastic Signals
143(15)
5.2.1 Mathematical Model
144(2)
5.2.2 Low Modulation Index
146(2)
5.2.3 Medium Modulation Index
148(3)
5.2.4 High Modulation Index
151(7)
5.3 Frequency and Phase Demodulation
158(4)
5.4 Performance Evaluation of Angle Modulation
162(2)
5.5 Angle Modulation with a Digital Signal
164(3)
6 Digital Modulation Theory 167(38)
6.1 Introduction
167(1)
6.2 Signal Space
167(11)
6.2.1 System Model
167(1)
6.2.2 Representation by Basis Functions
168(2)
6.2.3 Receiver Design and Sufficient Statistic
170(3)
6.2.4 Maximum Likelihood Decision
173(1)
6.2.5 Error Probability and the Union Bound
174(4)
6.3 Digital Modulation Schemes
178(5)
6.3.1 Pulse Amplitude Modulation
179(1)
6.3.2 Phase Shift Keying
180(1)
6.3.3 Quadrature Modulation
181(2)
6.4 Differential Coding
183(1)
6.5 Offset Phase Modulation
183(1)
6.6 The Transmission Pulse
184(2)
6.7 Constant Envelope Modulation
186(1)
6.8 The Rotated Constellation
187(7)
6.8.1 The Modulation Diversity Technique
188(1)
6.8.2 Rotating the QPSK Constellation
189(3)
6.8.3 The Presence of Channel Estimation Errors
192(1)
6.8.4 Simulation Results
192(2)
6.9 Orthogonal Frequency Division Multiplexing
194(11)
6.9.1 Description of OFDM
195(4)
6.9.2 COFDM Transmission
199(1)
6.9.3 OFDM with Random Signals
200(1)
6.9.4 Quadrature Modulation with Random Signals
200(5)
Appendix A: Fourier and Hilbert Transforms 205(10)
Appendix B: Biography of the Author 215(6)
Appendix C: Glossary 221(12)
References 233(8)
Index 241
Marcelo Sampaio de Alencar, Federal University of Bahia (UFBA), Brazil.