[sdiy] Digital 4 pole filter in an FPGA

[Rainer Buchty]

On Tue, 9 Dec 2008, Scott Gravenhorst wrote:

> I wonder if that could be a blessing in disguise since distortion will 
> generate additional harmonics...

Following Antti's DAFX papers, it's these distortions -- and where 
applied -- which e.g. makes the sonic difference between Moog and SSM 
filters, or which makes the difference between an "analog"/"warm" and a 
"digital"/"clean" sounding digital filter.

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.

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 
resulting signal is already decent enough, making it possible to just do 
a table-based distortion as opposed to approximating tanh() by x-x^3/6 
for x within [-1:1].

Rainer