Distortion
Description
Natural analog distortion
occurs when a device is fed an input signal with too high of a gain for it to
play cleanly. By playing ‘unreachably high’ levels as high as it can possibly
can, the overdriven device is forced to reshape the sound waves. The reshaping
reduces or ‘clips’ the top and bottom of the wave at its maximum and minimum
levels. Soft clipping reshapes the peaks of the curve smoothly while hard
clipping flattens them. Hard clipping reshapes the waveform to resemble a
square wave. The flatter the top of the curve, the ‘heavier’ or ‘harsher’ the
sound. The reshaped sound waves have their own set of harmonics, yielding
brilliant tones.
Digitally recreating
distortion involves mathematically modeling the clipped analog waveforms.
Adding odd-numbered sine wave partials yields a waveform resembling a square
wave. Adding even-numbered sine wave partials yields a waveform similar to a
triangle wave. Different combinations of partials yield different forms of
distortion. Csound has built-in distortion opcodes, but they are limited in the
sounds they can model. Many more varieties of distortion can be produced using
function tables to model distorted waveforms.
Graphical Depictions
Effect Formula
Since there is no ‘general’
distortion formula, this is one instance of a distorted waveform – the equations
behind the graphical depiction.
|
y[n] = f(x[n]) |
|
y[n] = output
signal |
|
x[n] = input
signal (triangle wave) |
|
f(x) = distortion
waveform model |
|
f(x) = -1 for x
< -1/2 |
|
f(x) = x for –1/2
< x < 1/2 |
|
f(x) = 1 for x
> 1/2 |
Source Code
(.csd files can be viewed with Notepad or any text
editor)
Example
Audio Clips
|
Original unprocessed
signal 1 |
|
|
Signal 1, light distortion |
|
|
Signal 1, medium
distortion |
|
|
Signal 1, heavy distortion |
|
|
Original unprocessed
signal 2 |
|
|
Signal 2, light distortion |
|
|
Signal 2, medium
distortion |
|
|
Signal 2, heavy distortion |
References
Lehman, Scott
(1996). Effects Explained. Harmony Central. Retrieved 6/04 from
http://www.harmony-central.com/Effects/effects-explained.html
Mikelson, Hans
(2000). Modeling a multieffects processor in Csound. In Boulanger,
Richard (2000), The Csound book (pp 575-594). Cambridge, MA: MIT Press.
Schindler,
Allan. (1998). Eastman Csound tutorial.
Eastman School of Music. Retrieved 6/04 from
http://www.esm.rochester.edu/onlinedocs/allan.cs/
Vercoe, Barry.
(1992). The public Csound reference manual, version 4.16. MIT Press.
Retrieved 6/04 from http://www.lakewoodsound.com/csound/hypertext/manual.htm
Zolzer, Udo.
(2002). Digital audio effects. West Sussex, England: Baffins Lane.