We can model dynamic range compression as a level-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.
Convolution Representation Summary
Series, Real, Second-Order Sections