# Variable-hardness clipping function¶

**Author or source:**Laurent de Soras (moc.ecrofmho@tnerual)**Created:**2004-04-07 09:36:46**Linked files:**`laurent.gif`

.

```
k >= 1 is the "clipping hardness". 1 gives a smooth clipping, and a high value gives
hardclipping.
Don't set k too high, because the formula use the pow() function, which use exp() and
would overflow easily. 100 seems to be a reasonable value for "hardclipping"
```

1 | ```
f (x) = sign (x) * pow (atan (pow (abs (x), k)), (1 / k));
``` |

## Comments¶

**Date**: 2003-11-15 03:56:35**By**: moc.liamtoh@sisehtnysorpitna

```
// Use this function instead of atan and see performance increase drastically :)
inline double fastatan( double x )
{
return (x / (1.0 + 0.28 * (x * x)));
}
```

**Date**: 2004-07-16 09:36:33**By**: gro.psdcisum@maps

```
The greater k becomes the lesser is the change in the form of f(x, k). I recommend using
f2(x, k2) = sign(x) * pow(atan(pow(abs(x), 1 / k2)), k2) , k2 in [0.01, 1]
where k2 is the "clipping softness" (k2 = 0.01 means "hardclipping", k2 = 1 means
"softclipping"). This gives better control over the clipping effect.
```

**Date**: 2004-08-12 18:42:58**By**: gro.liamon@demrofniton

```
Don't know if i understood ok , but, how can i clip at diferent levels than -1.0/1.0 using this
func? tried several ways but none seems to work
```

**Date**: 2004-08-14 04:02:00**By**: moc.liamg@noteex

```
The most straightforward way to adjust the level (x) at which the signal is clipped would be to
multiply the signal by 1/x before the clipping function then multiply it again by x afterwards.
```

**Date**: 2004-10-09 23:27:57**By**: ed.xmg@releuhcsc

```
Atan is a nice softclipping function, but you can do without pow().
x: input value
a: clipping factor (0 = none, infinity = hard)
ainv: 1/a
y = ainv * atan( x * a );
```

**Date**: 2006-05-28 20:32:49**By**: uh.etle.fni@yfoocs

```
Even better, you can normalize the output using:
shape = 1..infinity
precalc:
inv_atan_shape=1.0/atan(shape);
process:
output = inv_atan_shape * atan(input*shape);
This gives a very soft transition from no distortion to hard clipping.
```

**Date**: 2011-01-03 14:07:35**By**: moc.liamg@nalevart

```
Scoofy,
What do you mean with 'shape'?
Is it a new parameter?
```

**Date**: 2013-01-18 02:42:09**By**: moc.liamtoh@niffumtohrepus

```
sign (x) * pow (atan (pow (abs (x), k)), (1 / k));
OUCH! That's a lot of pow, atan and floating point division - probably kill most CPU's :) My
experience has been that any sigmoid function will create decent distortion if oversampled and
eq'ed properly. You can adjust the "hardness" of the clipping by simply changing a couple
coefficients, or by increasing/decreasing the input gain: like so:
y = A * tanh(B * x)
Cascading a couple/few of these will give you bone-crushing, Megadeth/Slayer style grind while
rolling back the gain gives a Fender Twin sound.
Two cascaded half-wave soft clippers gives duty-cycle modulation and a transfer curve similar to
the 3/2 power curve of tubes. I came up w/ a model based on that solution after reading reading
this: http://www.trueaudio.com/at_eetjlm.htm (orig. link at www.simulanalog.org)
```

**Date**: 2013-06-14 11:42:26**By**: moc.liamtoh@niffumtohrepus

```
If anyone is interested, I have a working amp modeler and various c/c++ classes that model
distortion circuits by numerical solutions to non-linear ODE's like those described by
Yeh, Smith, Macak, Pakarinen, et al. in their PhD disertations and DAFX papers. Although
static waveshapers/filters can give decent approximations & cool sounds, they lack the dynamic
properties of the actual circuits and have poor harmonics. I also have whitepapers on my
implementations for those that think math is cool. Drop me a line for more info.
```