Soft clipping is a type of distortion effect where the amplitude of a signal is saturated along a smooth curve, rather than the abrupt shape of hard-clipping. Soft clipping is similar to the type of distortion found in certain analog audio systems. Examples include a vacuum tube amplified and the saturation of magnetic tape.

There are many non-linear functions that can be used to digitally create a soft-clipping distortion effect. One example of soft-clipping distortion is based on using a cubic function. An equation to create soft-clipping is:

$output = input - \frac{1}{3} \cdot {(input)}^{3}$

By decreasing the scaling coefficient of the cubic term from $\frac{1}{3}$ to 0, the relative amount of distortion is reduced until the function becomes a linear equation.

A different method for creating soft-clipping distortion is based on the arctangent function. The relative amount of distortion can be set by the $\alpha$ coefficient.

$output = \frac{2}{\pi} \cdot arctan(\alpha \cdot input)$

Typical values of the $\alpha$ coefficient are on the order of $\alpha \in [1,10]$. For values of $\alpha >> 10$, the soft-clipping distortion approaches infinite clipping distortion.

Next, let’s look at another approach to creating distortion called bit reduction or bit crushing.