We can model dynamic range compression as an *amplitude-dependent
gain*. Multiplying a signal by a constant gain (``volume control''),
on the other hand, is a linear operation. Let's check that the
scaling and superposition properties of linear systems are satisfied
by a constant gain: For any signals , and for any constants
, we must have

Dynamic range compression can also be seen as a *time-varying
gain* factor, so one might be tempted to classify it as a linear,
time-varying filter. However, this would be incorrect because the
gain , which multiplies the input, *depends on the input
signal* . This happens because the compressor must estimate the
current signal level in order to normalize it. Dynamic range
compression can be expressed symbolically as a filter of the form

In general, any signal operation that includes a multiplication in which both multiplicands depend on the input signal can be shown to be nonlinear.

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