Page 125 - Fundamentals of Communications Systems

Chapter
4

Complex Baseband

Representation of Bandpass
Signals

4.1 Introduction
A majority of communication systems operate by modulating an information
bearing waveform onto a sinusoidal carrier. As examples, Table 4.1 lists the
carrier frequencies of various methods of electronic communication.
One can see by examining Table 4.1 that the carrier frequency of the trans-
mitted signal is not the component which contains the information. Instead it
is the signal modulated on the carrier which contains the information. Hence
a method of characterizing a communication signal, which is independent of
the carrier frequency, is desired. This has led communication system engineers
to use a complex baseband representation of communication signals to
simplify their job. All of the communication systems mentioned in Table 4.1
can be and typically are analyzed with this complex baseband representation.
This chapter develops the complex baseband representation for determinis-
tic signals. Other references that develop these topics well are [Pro89, PS94,
Hay83, BB99]. One advantage of the complex baseband representation is sim-
plicity. When communication system engineers use the complex baseband
notation, all signals are lowpass signals and the fundamental ideas behind
modulation and communication signal processing are easily developed. Also
digital processing based receivers use the complex baseband representation in
describing the baseband processing algorithms. In fact, complex baseband rep-
resentation is so prevalent in engineering systems that the most widely used
tool, Matlab, has been configured by default to process all variables in a pro-
gram as complex signals. Hopefully by the time you are done with this course
the utility of this view will be apparent.

4.1
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