Processing of Signals - Digital Signal Processing: A Practitioner's Approach - page 3

1.2.1 Spectral Domain
Signals are generated as a function of time (temporal domain) but it is often
convenient to analyse them as a function of frequency (spectral domain). Figure 1.1
shows a narrowband signal in the temporal domain and the spectral domain.
Figure 1.2 does the same for a broadband signal. For historical reasons, signals

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Broadband signal

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(a) (b)

Figure 1.2 Broadband signal x ð t Þ

which are classified by their spectral characteristics are more popular. Here are
some examples:

1. Band-limited signals
(a) Narrowband signals
(b) Wideband signals
2. Additive band-limited signals

1.2.1.1 Band-Limited Signals

Band-limited signals, narrow or wide, are the most commonly encountered signals
in real life. They could be a signal from an RF transmitter, the noise of an engine,
etc. The signals in Figures 1.1 and 1.2 are essentially the same except that their
bandwidths are different and cannot be perceived in the time domain. Only by
obtaining the spectral characteristics using the Fourier transform we can distinguish
one from the other.

1.2.1.2 Additive Band-Limited Signals

A group of additive band-limited signals are conventionally known as composite
signals with a wide range of frequencies. Typically, a signal emitted from a radar [1]
and its reflection from the target have a carrier frequency of a few gigahertz and a
pulse repetition frequency (PRF) measured in kilohertz. The rotation frequency of