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. (It only has any effect when the signal is amplified so that it peaks beyond [-1,1].)
• f(x) = x if -1 < x < 1; -x - 2 if x < -1; -x + 2 if x > 1 is "fold distortion," which is similar to clip distortion but even buzzier.
• f(x) = x if -1 < x < 1; x + 2 if x < -1; x - 2 if x > 1 is "wrap distortion," which is buzzier and harsher still than fold distortion.
• f(x) = tanh(x) (hyperbolic tangent) is quite a bit like clip distortion, but much, much subtler. It is a form of "soft clipping."
• 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.