The envelope
Many application measurements result in a time signal containing a rapidly oscillating component. The
amplitude of the oscillation varies
slowly with time, and the shape of
the slow time variation is called the
“envelope”. The envelope often contains important information about
the signal. By using the Hilbert
transform, the rapid oscillations can
be removed from the signal to produce a direct representation of the
envelope alone.
For example, the impulse response
of a single degree of freedom system
is an exponentially damped sinusoid,
. This is shown as (a) in Fig. 1.
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