[sdiy] Digital 4 pole filter in an FPGA

[Magnus Danielson]

Antti Huovilainen skrev:
> On Tue, 9 Dec 2008, Rainer Buchty wrote:
> 
>> For me, it was amazing to see that whenever the attribute "warmth" comes
>> up, it is related to a tanh()-shaped compression function, no matter
>> whether it's tube-based distortion, analog tape saturation, or
>> distortion within the filter.
> 
> Tanh has nothing to do with tubes.

Agreed...

> Quite asymmetric curves there (just 
> to nitpick). For differential transistor circuits it can be derived 
> directly from the transfer function (with only minor approximations).

To nitpick some more... the transistors do not display tanh curves 
themselfs, they have exp responses. It is the result of a balanced 
transistor pair that produces the tanh response. A tube-pair would 
produce something similar if hooked up similar, which is not that 
uncommmon actually. Quad-II amps and HP200CD oscillators spring to mind.

When the transitor has the classical NP-relation

I = I_s * [ exp (qV/kT) - 1 ]

the tube has a similar behaviour

I = k * (E_k + my * E_g)^3/2

The diffrential forms look kind of similar...

However, there exist many tube circuits that are not balanced, and then the

> In 
> tape saturation it's probably not strictly correct but the shape is 
> smooth and distortion increases gradually so it largely does the job.

It is fairly smooth, but fine-grained it is not... hence the need for 
bias signal and also the noise.

>> For any FPGA implementation the question therefore is how to get tanh()
>> as cheap as possible. Maybe just shaping the upper 8 bits of the
> 
> Use a small lookup table with linear interpolation. You only need one 
> side since it's symmetric and I assume bit operations are dirt cheap in 
> FPGA (abs and neg).

Sounds reasnoble. Another approach is to use a lookup table to provide a 
multiplicative term for the signal. Could potentially provide good 
quality for a smaller table.

Cheers,
Magnus