11. Continuous-Time Fourier Transform
In previous chapters, our presentation of the spectrum
was limited to sinusoids and periodic signals. Now we
want to develop
a completely general definition of the
frequency spectrum that will apply to any signal
x(t).
Armed with this powerful tool, we will be able to:
-
define a precise notion of bandwidth for a signal,
-
explain the inner workings of modern communication
systems which are able to transmit many signals at
one time by sharing the available bandwidth, and
-
define filtering operations that are needed to separate
signals in such frequency-shared systems.
There are
many other applications of the Fourier transform, so
it is safe to say that Fourier analysis provides the
rigorous language needed to define and design modern
engineering systems.
