[sdiy] Fast envelope generation

[Richie Burnett]

> From: "Donald Tillman" <don at till.com>
>
> ...As the voltage on a cap rises, the difference between the source 
> voltage and the cap voltage is less,
> and thus the charging current through the resistor is less, so the voltage 
> rises slower.  Repeat.
> So all you really need to do is duplicate that process: on each iteration 
> take the difference between the
> source voltage and cap voltage, scale that by the time constant, and add 
> that to the cap voltage each time.

That's exactly what the IIR filter equation implements.  Rewritten in terms 
of capacitor voltage Vc and input voltage Vi.

Vc = Vc + r * (Vi - Vc)

But, for the reasons Tom Wiltshire stated the simple difference equation 
might not be the easiest or most flexible way of arriving at the desired 
result on a low-end 8-bit microcontroller with limited maths capabilities.

At the end of the day you can burn ROM and just read from a huge exponential 
lookup-table, _OR_ have a smaller LUT and some clever bit shifting and 
interpolation in software, _OR_ do it all in maths without any LUT at all. 
How you use your ROM, RAM and CPU cycles is as ever the designers choice :-)

-Richie,