**Description:**

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, 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
books covers signal representations for most known waveforms, 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.

Contents:

**Preface **

**List of Figures **

**Chapter 1: Theory of Signals and Linear Systems** •
Introduction • Signal Analysis • Linearity • The Convolution Theorem • Some
Important Functions • The Constant Function • The Sine and the Cosine Functions
• The Heaviside Step Function • The Ramp Function • The Gate Function • Impulse
Function or Dirac’s Delta Function • The Sampling Function • Even and Odd
Functions • Some Elementary Properties of Functions • Basic Fourier Analysis •
The Trigonometric Fourier Series • The Compact Fourier Series • The Exponential
Fourier Series • Fourier Transform • Bilateral Exponential Signal • Transform
of the Gate Function • Fourier Transform of the Impulse Function • Transform of
the Constant Function • Fourier Transform of the Sine and Cosine Functions •
Fourier Transform of the Complex Exponential • Fourier Transform of a Periodic
Function • Some Properties of the Fourier Transform • Linearity of the Fourier
Transform • Scaling Property • Symmetry of the Fourier Transform • Time Domain
Shift • Frequency Domain Shift • Differentiation in the Time Domain •
Integration in the Time Domain • The Convolution Theorem in the Time Domain •
The Convolution Theorem in the Frequency Domain • The Sampling Theorem •
Parseval’s Theorem • Average, Power, and Autocorrelation • Time Autocorrelation
of Signals

**Chapter 2: Random Signals and Noise** •
The Theory of Sets, Functions, and Measure • Set Theory • Operations on Sets •
Families of Sets • Indexing Sets • Algebra of Sets • Borel Algebra •
Probability Theory • Axiomatic Approach to Probability • Bayes’ Rule • Random
Variables • Mean Value of a Random Variable • Moments of a Random Variable •
The Variance of a Random Variable • The Characteristic Function of a Random
Variable • Some Important Random Variables • Joint Random Variables •
Stochastic Processes • The Autocorrelation Function • Stationarity • Wide Sense
Stationarity • Ergodic Signals • Properties of the Autocorrelation • The Power
Spectral Density • Properties of the Power Spectral Density • Linear Systems •
Expected Value of the Output Signal • The Response of Linear Systems to Random
Signals • Phase Information • Analysis of a Digital Signal • Autocorrelation of
a Digital Signal • Power Spectral Density for the Digital Signal • The Digital
Signal Bandwidth • Non-Linear Systems • The Two-Level Quantizer • Quantization
Noise Spectrum for a Two-level Quantizer • Response of a Squarer Circuit •
Response of a Non-Linear Amplifier • Response of an Ideal Diode

**Chapter 3: Amplitude Modulation Theory** •
Introduction • Amplitude Modulation • Amplitude Modulation by Random Signals •
Power of an AM Carrier • Power Spectral Density • Amplitude Modulators •
Quadratic Modulator • Synchronous Modulator • Digital AM Signal • AM
Transmitter • Suppressed Carrier Amplitude Modulation • Spectrum of the AM-SC
Signal • Power Spectral Density • The AM-SC Modulator • AM-VSB Modulation •
Amplitude Demodulation • Noise Performance of Amplitude Modulation

**Chapter 4: Quadrature Amplitude Modulation Theory** •
Quadrature Modulation with Random Signals • Single Sideband Modulation •
Hilbert Transform • Fourier Transform of 1/ p*t *• Properties of the
Hilbert Transform • Producing the SSB Signal • Lower Sideband SSB with Random
Signal • ISB Modulation • AM-Stereo • Quadrature Amplitude Demodulation •
Performance Evaluation of SSB • Digital Quadrature Modulation

**Chapter 5: Angle Modulation Theory** •
Introduction • Angle Modulation with Stochastic Signals • Mathematical Model •
Low Modulation Index • Medium Modulation Index • High Modulation Index •
Frequency and Phase Demodulation • Performance Evaluation of Angle Modulation •
Angle Modulation with a Digital Signal

**Chapter 6: Digital Modulation Theory** •
Introduction • Signal Space • System Model • Representation by Basis Functions
• Receiver Design and Sufficient Statistic • Maximum Likelihood Decision •
Error Probability and the Union Bound • Digital Modulation Schemes • Pulse
Amplitude Modulation • Phase Shift Keying • Quadrature Modulation •
Differential Coding • Offset Phase Modulation • The Transmission Pulse •
Constant Envelope Modulation • The Rotated Constellation • The Modulation
Diversity Technique • Rotating the QPSK Constellation • The Presence of Channel
Estimation Errors • Simulation Results • Orthogonal Frequency Division
Multiplexing • Description of OFDM • COFDM Transmission • OFDM with Random
Signals • Quadrature Modulation with Random Signals

**Appendix A: Fourier and Hilbert Transforms **

**Appendix B: Biography of the Author **

**Appendix C: Glossary **

**References **

**Index **

About the Author:

**Marcelo Sampaio de Alencar, **Federal
University of Bahia (UFBA), Brazil

Target Audience:

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.