
14.3. Fourier Transforms 189
14.3. Fourier Transforms
The most general transforms for an arbitrary function of time create a
continuum of frequency components in the complex plane. These
transforms, shown in Fig. 14.6, can be applied to aperiodic functions
to determine their frequency spectra, and the complex operator,
s
, can
be replaced by
j
ω
for this purpose. Integration in the complex plane
can be accomplished numerically with the integration carried out to
the maximum frequency of interest.
Several simple examples will be used to show the general behavior
of these integrals. The first, at left in Fig. 14.7, is a pulse of unit area
in the time ...