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C h a p t e r
SIGNALS AND SPECTRA
CHAPTER OBJECTIVES
• Basic signal properties (DC, RMS, dBm, and power)
• Fourier transform and spectra
• Linear systems and linear distortion
• Bandlimited signals and sampling
• Discrete Fourier transform
• Bandwidth of signals
2–1 PROPERTIES OF SIGNALS AND NOISE
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In communication systems, the received waveform is usually categorized into the desired part
containing the information and the extraneous or undesired part. The desired part is called the
signal, and the undesired part is called noise.
This chapter develops mathematical tools that are used to describe signals and noise
from a deterministic waveform point of view. (The random waveform approach is given in
Chapter 6.) The waveforms will be represented by direct mathematical expressions or by the
use of orthogonal series representations such as the Fourier series. Properties of these waveforms,
such as their DC value, root-mean-square (RMS) value, normalized power, magnitude
spectrum, phase spectrum, power spectral density, and bandwidth, will also be established. In
addition, effects of linear filtering will be studied.
The waveform of interest may be the voltage as a function of time, v(t), or the current as
a function of time, i(t). Often, the same mathematical techniques can be used when one is
working with either type of waveform. Thus, for generality, waveforms will be denoted simply
as w(t) when the analysis applies to either case.