Distortion

Distortion can refer to a variety of mathematically distinct effects, referring to an aesthetic associated with warmth, fuzziness, dirtiness, harshness.

One generic method for achieving distortion digitally is to use a "non-linear transfer function," a memoryless filter that maps amplitudes from an input signal to an output signal according to a deterministic function. As the name implies, we exclude any boring linear functions that only serve to amplify or attenuate. Many non-linear transfer functions can be used, with different effects:

• f(x) = x if -1 < x < 1; -1 if x < -1; 1 if x > 1 is "clip distortion," which can occur naturally when digital audio caps. It is ringy and tends to add odd harmonics.
• f(x) = tanh(x) (hyperbolic tangent) is quite a bit like clip distortion, but much, much subtler.
• f(x) = 0 if x = 0; 1 - x if x > 0; -1 - x if x < 0 is "inside-out distortion," which generates extremely abrasive and noisy audio. Good shit.