Modulation Theory.

Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- List of Figures -- 1: Theory of Signals and Linear Systems -- 1.1 Introduction -- 1.2 Signal Analysis -- 1.2.1 Linearity -- 1.2.2 The Convolution Theorem -- 1.3 Some Important Functions -- 1.3.1 The Constant Function -- 1.3.2 The Sine and the Cosine Functions -- 1.3.3 The Heaviside Step Function -- 1.3.4 The Ramp Function -- 1.3.5 The Gate Function -- 1.3.6 Impulse Function or Dirac's Delta Function -- 1.3.7 The Sampling Function -- 1.3.8 Even and Odd Functions -- 1.3.9 Some Elementary Properties of Functions -- 1.4 Basic Fourier Analysis -- 1.4.1 The Trigonometric Fourier Series -- 1.4.2 The Compact Fourier Series -- 1.4.3 The Exponential Fourier Series -- 1.5 Fourier Transform -- 1.5.1 Bilateral Exponential Signal -- 1.5.2 Transform of the Gate Function -- 1.5.3 Fourier Transform of the Impulse Function -- 1.5.4 Transform of the Constant Function -- 1.5.5 Fourier Transform of the Sine and Cosine Functions -- 1.5.6 Fourier Transform of the Complex Exponential -- 1.5.7 Fourier Transform of a Periodic Function -- 1.6 Some Properties of the Fourier Transform -- 1.6.1 Linearity of the Fourier Transform -- 1.6.2 Scaling Property -- 1.6.3 Symmetry of the Fourier Transform -- 1.6.4 Time Domain Shift -- 1.6.5 Frequency Domain Shift -- 1.6.6 Differentiation in the Time Domain -- 1.6.7 Integration in the Time Domain -- 1.6.8 The Convolution Theorem in the Time Domain -- 1.6.9 The Convolution Theorem in the Frequency Domain -- 1.7 The Sampling Theorem -- 1.8 Parseval's Theorem -- 1.9 Average, Power, and Autocorrelation -- 1.9.1 Time Autocorrelation of Signals -- 2: Random Signals and Noise -- 2.1 The Theory of Sets, Functions, and Measure -- 2.1.1 Set Theory -- 2.1.2 Operations on Sets -- 2.1.3 Families of Sets -- 2.1.4 Indexing Sets.

2.1.5 Algebra of Sets -- 2.1.6 Borel Algebra -- 2.2 Probability Theory -- 2.2.1 Axiomatic Approach to Probability -- 2.2.2 Bayes' Rule -- 2.3 Random Variables -- 2.3.1 Mean Value of a Random Variable -- 2.3.2 Moments of a Random Variable -- 2.3.3 The Variance of a Random Variable -- 2.3.4 The Characteristic Function of a Random Variable -- 2.3.5 Some Important Random Variables -- 2.3.6 Joint Random Variables -- 2.4 Stochastic Processes -- 2.4.1 The Autocorrelation Function -- 2.4.2 Stationarity -- 2.4.3 Wide Sense Stationarity -- 2.4.4 Ergodic Signals -- 2.4.5 Properties of the Autocorrelation -- 2.4.6 The Power Spectral Density -- 2.4.7 Properties of the Power Spectral Density -- 2.5 Linear Systems -- 2.5.1 Expected Value of the Output Signal -- 2.5.2 The Response of Linear Systems to Random Signals -- 2.5.3 Phase Information -- 2.6 Analysis of a Digital Signal -- 2.6.1 Autocorrelation of a Digital Signal -- 2.6.2 Power Spectral Density for the Digital Signal -- 2.6.3 The Digital Signal Bandwidth -- 2.7 Non-Linear Systems -- 2.7.1 The Two-Level Quantizer -- 2.7.2 Quantization Noise Spectrum for a Two-level Quantizer -- 2.7.3 Response of a Squarer Circuit -- 2.7.4 Response of a Non-Linear Amplifier -- 2.7.5 Response of an Ideal Diode -- 3: Amplitude Modulation Theory -- 3.1 Introduction -- 3.2 Amplitude Modulation -- 3.3 Amplitude Modulation by Random Signals -- 3.3.1 Power of an AM Carrier -- 3.3.2 Power Spectral Density -- 3.4 Amplitude Modulators -- 3.4.1 Quadratic Modulator -- 3.4.2 Synchronous Modulator -- 3.4.3 Digital AM Signal -- 3.4.4 AM Transmitter -- 3.5 Suppressed Carrier Amplitude Modulation -- 3.6 Spectrum of the AM-SC Signal -- 3.6.1 Power Spectral Density -- 3.6.2 The AM-SC Modulator -- 3.7 AM-VSB Modulation -- 3.8 Amplitude Demodulation -- 3.9 Noise Performance of Amplitude Modulation -- 4: Quadrature Amplitude Modulation Theory.

4.1 Quadrature Modulation with Random Signals -- 4.2 Single Sideband Modulation -- 4.2.1 Hilbert Transform -- 4.2.2 Fourier Transform of 1/πt -- 4.2.3 Properties of the Hilbert Transform -- 4.2.4 Producing the SSB Signal -- 4.2.5 Lower Sideband SSB with Random Signal -- 4.3 ISB Modulation -- 4.4 AM-Stereo -- 4.5 Quadrature Amplitude Demodulation -- 4.6 Performance Evaluation of SSB -- 4.7 Digital Quadrature Modulation -- 5: Angle Modulation Theory -- 5.1 Introduction -- 5.2 Angle Modulation with Stochastic Signals -- 5.2.1 Mathematical Model -- 5.2.2 Low Modulation Index -- 5.2.3 Medium Modulation Index -- 5.2.4 High Modulation Index -- 5.3 Frequency and Phase Demodulation -- 5.4 Performance Evaluation of Angle Modulation -- 5.5 Angle Modulation with a Digital Signal -- 6: Digital Modulation Theory -- 6.1 Introduction -- 6.2 Signal Space -- 6.2.1 System Model -- 6.2.2 Representation by Basis Functions -- 6.2.3 Receiver Design and Sufficient Statistic -- 6.2.4 Maximum Likelihood Decision -- 6.2.5 Error Probability and the Union Bound -- 6.3 Digital Modulation Schemes -- 6.3.1 Pulse Amplitude Modulation -- 6.3.2 Phase Shift Keying -- 6.3.3 Quadrature Modulation -- 6.4 Differential Coding -- 6.5 Offset Phase Modulation -- 6.6 The Transmission Pulse -- 6.7 Constant Envelope Modulation -- 6.8 The Rotated Constellation -- 6.8.1 The Modulation Diversity Technique -- 6.8.2 Rotating the QPSK Constellation -- 6.8.3 The Presence of Channel Estimation Errors -- 6.8.4 Simulation Results -- 6.9 Orthogonal Frequency Division Multiplexing -- 6.9.1 Description of OFDM -- 6.9.2 COFDM Transmission -- 6.9.3 OFDM with Random Signals -- 6.9.4 Quadrature Modulation with Random Signals -- Appendix A: Fourier and Hilbert Transforms -- Appendix B: Biography of the Author -- Appendix C: Glossary -- References -- Index.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.