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variableamplitude

Variable amplitude refers to a condition in which the magnitude of a waveform changes over time or along a spatial dimension. For a time-domain signal, the instantaneous amplitude A(t) defines how large the oscillations are at each moment, producing an envelope that bounds the oscillations. If A(t) is constant, the signal has fixed amplitude; when it varies, the amplitude is variable. A common mathematical form is x(t) = A(t) cos(ω0 t + φ(t)), where A(t) ≥ 0 represents the envelope and φ(t) is a phase function. When the amplitude is modulated by another signal, the process is called amplitude modulation (AM), widely used to transmit information by varying the carrier amplitude according to the modulating signal.

In engineering and physics, variable amplitude occurs in both transient and steady-state regimes. It can arise

Applications and considerations vary by field. In communications, variable amplitude interacts with dynamic range and distortion;

from
changing
driving
forces,
damping,
nonlinearities,
or
path
losses.
The
envelope
of
a
variable-amplitude
signal
can
be
analyzed
to
extract
information
about
the
modulation
or
the
underlying
system
behavior.
Techniques
such
as
envelope
detection
or
the
Hilbert
transform
help
obtain
the
analytic
signal
and
instantaneous
amplitude,
while
time-varying
peak
or
RMS
measurements
describe
the
variation
quantitatively.
in
audio
processing,
it
reflects
expressive
dynamics;
in
seismology
and
vibration
analysis,
amplitude
changes
relate
to
source
characteristics
and
propagation
effects.
See
also
amplitude
modulation,
envelope,
and
modulation
index.