Page 44 - Fundamentals of Communications Systems

1.10 Chapter One

the presence of noise is completed. At this point an understanding of the trade-
offs associated with analog communications can be completed and interpreted.

1.5.4 Fundamentals of Digital Communication
This part of the book consists of six chapters that introduce the theory of dig-
ital communication. The first chapter of this part of the book again presents
the performance metrics in communications: fidelity, complexity, and spectral
efficiency and reinterprets these metrics for digital communications. This re-
emphasizes the trade-off first introduced with analog modulation. Interestingly
there is a more powerful statement, due to Claude Shannon, that can be made
about the achievable fidelity and spectral efficiency that will frame this in-
troductory presentation of digital communication presented in this book. The
following chapter introduces the classic methods of communicating 1 bit of in-
formation. This is developed by going through a five-step design process. The
digital communication design problem is generalized for the transmission of
multiple bits of information in the following chapter. The unfortunate situation
exists with multiple bit transmission that the complexity of the optimum de-
coder grows exponentially with the number of bits to be transmitted. To address
this exponential growth in complexity, signal structures that offer reduced com-
plexity optimum demodulation structures are introduced. Several examples of
these reduced complexity modulations that are used in engineering practice are
introduced and these examples are considered in detail. The penultimate chap-
ter of the book considers techniques to greatly improve the spectral efficiency
of digital communications. A section of this part of the book considers the tools
used to test digital communication systems in practice. The ideas and uses of
the vector diagram and the eye diagram in the testing of digital communication
systems are explained and motivated. The idea of modulations with memory,
which provides the structure to approach Shannon’s bounds on communication
fidelity and spectral efficiency, are briefly introduced in the final chapter.
Now on to the fun stuff!

1.6 Homework Problems
Problem 1.1. Research the following person whose letter matches the first letter
of your last name and write a paragraph about why they were important in
communication theory.
(a) Jean Baptiste Joseph Fourier (b) Antoine Parseval (c) John R. Carson
(d) Friedrich Wilhelm Bessel (e) John William Strutt (f) Samuel B. Morse
(g) Emile Baudot (h) Georg Simon Ohm (i) Reginald Fessenden
(j) Stephen O. Rice (k) Claude Shannon (l) Alexander Graham Bell
(m) Hedy Lamarr (n) Claude Berrou (o) Lee de Forest
(p) Harold Nyquist (q) Andrei Andreyevich Markov (r) Reverend Thomas Bayes
(s) Gottfried Wilhelm Leibniz (t) Carl Friedrich Gauss (u) Pierre Simon Laplace
(v) Christian Doppler (w) Norbert Wiener (x) David Hilbert
(y) Gordon Moore (z) Euclid of Alexandria