Page 16 - Optical Communications Essentials

Basic Concepts of Communication Systems

6 Chapter One

Amplitude Amplitude

0 Time 0 Time

(a) 0° 1/4 cycle (b) 90°

Amplitude Amplitude

0 Time 0 Time

1/2 cycle (c) 180° (d) 270°

Addition of two waves that are
π radians out of phase yields
zero final amplitude
Figure 1.4. Examples of phase differences between two sine waves. Two waves that
are 180° out of phase will add destructively.

importance when one is considering the operation of optical couplers, as
described in Chap. 8.

Example
■ A sine wave has a frequency f 5kHz. Its period is T 1/5000s 0.20ms.
■ A sine wave has a period T 1ns. Its frequency is f 1/(10 9 s) 1GHz.
1
■ A sine wave is offset by /4 cycle with respect to time 0. Since 1 cycle is 360°, the phase
shift is φ 0.25 360° 90° π/2 rad.
Two further common characteristics in communications are the frequency
spectrum (or simply spectrum) and the bandwidth of a signal. The spectrum of
a signal is the range of frequencies that it contains. That is, the spectrum of a
signal is the combination of all the individual sine waves of different frequencies
which make up that signal. The bandwidth (designated by B) refers to the width
of this spectrum.

Example If the spectrum of a signal ranges from its lowest frequency f low 2kHz to
its highest frequency f high 22kHz, then the bandwidth B f high f low 20kHz.

1.3. Digital Signal Formats
A digital signal is an ordered sequence of discrete symbols selected from a finite
set of elements. Examples of digital signals include the letters of an alphabet,

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