There are many types of distortion effects used in audio. Each type of distortion produces different results when processing signals.
There are a couple different ways to analyze the differences between the distortion effects. One way is to visualize the output amplitude versus the input amplitude of the effect. In this case, a plot of the processing I/O Characteristics is used.
Another way is to compare the harmonics created by processing a sine wave with the effect. This can be done using a spectrum analyzer to display the amplitude of the different frequencies in the distorted signal.
An important concept that comes up in both analyses, is even and odd types of distortion.
For certain types of distortion, harmonics at even multiples of the input signal’s frequency are created. For other types, harmonics at odd multiples of the input signal’s frequency occur.
The way to determine what type of harmonics will occur for a distortion effect is to consider the relationship between the output amplitude and the input amplitude.
When this relationship can be described mathematically by an even function, then even harmonics occur. This type of function is symmetric when reflected across the y-axis in a plot. The definition for an even function is:
When the distortion effect can be described mathematically by an odd function, then odd harmonics occur. This type of function is circularly symmetric when rotated around the origin of a plot. The definition for an odd function is: