[sdiy] tanh distortion in a filter

[Tom Wiltshire]

On 11 Aug 2011, at 13:15, Olivier Gillet wrote:

>>> Can I just ask if there's anything particularly special about tanh in this
>>> situation?
>>> 
>>> It seems to me that you could use pretty much any sigmoid function.
> 
> tanh is what's actually happening in an analog system. If you are not
> concerned about exact modeling of the analog system, you can use
> another clipping function, for example a lowly (x - x ^ 3 / 6) (as
> used in csound) or x / sqrt(1 + x ^ 2) (as used in bristol), or some
> crazy rational fractions
> (http://www.kvraudio.com/forum/viewtopic.php?t=262823)

Aren't you and Neil confusing the model with the reality? If I've got it right, it's tanh because that comes from the standard model of the bipolar differential pair. As it says in the paper, this is "with some simplifying assumptions".
Fair enough if tanh is the closest model we've got to "ideal" transistor behaviour, but it doesn't have any particular legitimacy as soon as we decide that what we're modelling isn't an OTA - for example, a filter based on tube VCA integrators, or one based on my new patented "Zontron" gain-control element. Does it?
As soon as we're in the digital domain rather than trying to explain/predict the behaviour of an actual circuit, we can alter our model to suit ourselves and don't have to worry about what components that would represent in reality (aka "who cares if it's not an OTA if it sounds good").

For example, you could also try:

y = 1.2sin(x) / 0.2 + |sin(x)|

or even:

y = x^1/3

These aren't going to model any standard analog filter, but unless that's the specific aim, that doesn't matter. Or have I got the stick by the sticky end?

Thanks,
Tom