#### Preface

Prof. Dr. Khamies Mohammed Ali El-Shennawy, the author, believes that the book:
“Communication Theory and Signal Processing for Transform Coding”, is tailored for
the requirements of the individual area of the signal processing in communication
systems. The students of the undergraduate studies in the institutes, colleges,
universities, and academies and want to specialize in the field of communication
systems and signal processing, this book, is their innovation, and is more essential to
them before the entrance of their specialized work in communication systems, in order
to get the talent and the ability to have the faster solution for all the problems in
analog and digital communication and their applications. Prof. El-Shennawy teach
to the students of the undergraduate studies: circuit theory, communication theory,
communication systems, data communication, electro-magnetic, antennas, and
acoustics, and supervise the graduation projects as applications of Surface Acoustic
Wave SAW devices in communication systems, communication security systems
(encryption and decryption techniques, stream cipher, Data Encryption Standard DES,
public key encryption, factorization and logarithmic and elliptic curve encryption and
signature techniques, advanced encryption standard), global maritime distress and
safety systems, electronic chart display and information systems, global positioning
systems, air-borne and space-borne remote sensing. Also supervise and teach to the
students of the graduate and post graduate studies for diploma of high studies, M.Sc.
and Ph.D. courses: communication intelligence, data computer communication, surface
acoustic wave devices and charge coupled devices in modern communication systems,
ultra wide band technique, speech and digital coding, voice over internet protocol, audio
and video compression (transform coding), source coding techniques, speech and
digital watermarking, in the Arab Academy for Science and Technology and Maritime
Transport AASTMT, College of Engineering and Technology, Department of
Communication & Electronics and Computer Studies, Alexandria, Egypt, since 1988
to 2014 and still, three semesters every year.

This book contains a great number of numerous examples and solved problems and
exercises, to explain the methodology of Fourier analysis, Fourier series, Fourier
transform and properties, Discrete Fourier Transform DFT, Fast Fourier Transform
FFT, Discrete Cosine Transform DCT, Discrete Wavelet Transform DWT, Contourlet
Transform CT. The book proves that the students need mathematics in communication
more than you may think, and make the student has the ability to deal with the DFT,
FFT, DCT, DWT, and CT, utility computer programs. The advantage of this book is
the simplicity, attract the student, easy to solve the problems using different ways, and
with its wider contents in communication theory, applied in communication systems.

Also, this book is beneficial to the engineers of the graduate and post graduate studies,
and to the researchers in the research centers because the book contains a great number
of mathematical operations and is considered very important in the research results,
solving their problems. The book is a big jump to the students and engineers in
understanding, realization, and makes the understanding of their prediction fields wider.
The book is a very good chance to the students and the engineers for verifying their
predictive results in the communication problems and give them more trust. The book
is considered, the first step, mathematically solving the communication problems.

Chapter I is an introduction to the model of communication system, signal
contamination, why modulation and demodulation, Shannon-Hartley theorem, some
basics concepts of signals and classification of signals waveforms: periodic and
unperiodic, deterministic and random, Dirac delta function, unit step function, power
and energy, causal and non-causal, analog and digital, and low-pass and band-pass
signals, and five solved problems, as well as numerical examples.

Chapter II is review of the classical methods for the spectral analysis of the Fourier
series and power spectra, Fourier series real coefficients and complex exponential
coefficient methods, orthogonality, spectrum of periodic signals (discrete spectrum),
sinc function, Parseval`s power theorem, power spectral density, and eleven solved
problems, as well as numerical examples.

Chapter III is devoted to the spectral analyses of Fourier transform and energy spectra,
spectrum of unperiodic signals (continuous spectrum), spectrum of some important
integrable signals, rectangular pulse and sinc spectra, triangle pulse and sinc squared
spectra, Gaussian pulse and Gaussian spectra, radio frequency pulse and two sinc
spectra, decaying and rising single sided exponential pulses, Fourier transform
properties, linearity, duality, scaling, shifting, differentiation, integration property of
the zero boundary condition functions, convolution, area, and conjugate properties,
Rayleigh`s energy theorem, energy spectral density, Fourier transform of the real and
imaginary parts of a time function, and twenty eight solved problems, as well as
numerical examples.

Chapter IV presents the Fourier transform of the special functions (non-integrable
signals), Dirac delta function, exponential and sinusoidal functions, signum function,
and unit step function. Also the chapter presents the Fourier transform integration
property of the non-zero boundary condition functions, the relation between the Dirac
delta function and the unit step function, Fourier transform of the error function, and
twenty one solved problems, as well as numerical examples.

Chapter V evaluates the spectral analysis of the periodic signals using Fourier
transformation, periodic Dirac delta functions, periodic rectangular functions, periodic
triangle functions and six solved problems.

Chapter VI analysis the correlation function and spectral density, energy spectral
density, power spectral density, autocorrelation function of energy signals, Fourier
transform of autocorrelation function for energy signals, evaluation of energy content
in terms of autocorrelation function, autocorrelation function of power signals,
periodicity of autocorrelation function for power signals, Fourier transform of
autocorrelation function for power signals, evaluation of average power in terms of
autocorrelation function, cross-correlation function, cross-correlation function of
energy signals, Fourier transform of cross-correlation function for energy signals, cross
spectral density of energy signals, orthogonal energy signals in terms of crosscorrelation
function, cross-correlation function of power signals, Fourier transform of
cross-correlation function for power signals, cross spectral density of power signals,
orthogonal power signals in terms of cross-correlation function, and twenty three solved
problems.

Chapter VII shows the signal transmission and systems, impulse response, transfer
function, cascaded systems, causal and non-causal systems, stable and non-stable
systems, bandwidth of low-pass and band-pass systems, relation between input and
output energy spectral densities, distortionless system, ideal low-pass filter, ideal bandpass
filter, distortion systems, amplitude distortion, phase distortion, uniformly
distributed resistance capacitance interconnects systems, and sixteen solved problems.

Chapter VIII describes the Hilbert transform, Hilbert transform of sinusoidal functions,
Hilbert transform and orthogonality, Hilbert transform and convolution principle,
Hilbert transform of narrow band-pass signals, some important Hilbert transforms, and
four solved problems, as well as numerical examples.

Chapter IX explains different analysis of the narrow band-pass signals and systems,
pre-envelope, complex envelope, natural envelope, band-pass systems, equivalent lowpass
technique, new design criterion for band-pass systems (Kham-Shen Criteria),
input/output pre-envelope technique, dispersive systems, and envelope delay (group
delay), and seven solved problems, as well as numerical examples.

Chapter X illustrates the numerical computation of the Fourier transform, sampling
theorem, discrete Fourier transform and properties (linearity, shifting, and circular
convolution), fast Fourier transform, sine and cosine transforms, discrete cosine
transform, drawbacks of Fourier transform, short time Fourier transform, wavelet
transform, discrete wavelet transform, contourlet transform, some application of
compression techniques, lossless and lossy coding, Huffman encoding, run length
encoding, Lempel-Ziv-Wekh encoding, predictive encoding, delta encoding,
drawbacks of compression techniques, audio compression, MPEG layers I, II, III of
audio compression, video compression, Joint Photographic Experts Group JPEG, JPEG
initiative (JPEG 2000), Moving Picture Experts Group MPEG, MPEG-2, MPEG-4,
principles behind compression, MPEG-4 International Standard (MP4), Transformdomain
weighted interleave Vector Quantization TwinVQ in MPEG-4, comparison of
MPEG-4 (H.264) and JPEG-2000 video compression, and fourteen solved problems,
as well as numerical examples.

The ten chapters of the book are essentially suited for two semesters. The first semester
on communication theory (from chapter one to chapter nine). It is expected that the
reader has knowledge of mathematics, electronics, and circuit theory. The second
semester on signal processing, audio and image processing, numerical computation,
transform coding and compression techniques (chapter ten). The book is characterized
by three directions, the mathematical point of view, the communication theory point of
view, and the utility computer programs. The make up of the material for each course
may be determined only by the backgrounds and interests, thereby allowing
considerable flexibility in making up the course material. As an aid to the teacher of
each course, a detailed solutions manual for all the unsolved problems which at the end
of the chapters, is available from the publisher.

**Prof. Dr. Khamies M. A. El-Shennawy**

President Assistant

Arab Academy for Science and

Technology and Maritime Transport.

P.O.Box 1029, Alexandria, Egypt.

khamies@ieee.org