KVR Audio

Miles1981 · Post by **Miles1981** » Tue Oct 07, 2014 9:09 am

Agreed. Especially the osciallations at the start of the ramp are not nice.
The other distortion function (SD1) is more pleasant :p

itoa · Post by **itoa** » Tue Oct 07, 2014 9:14 am

I think this can be solved without iterations, just wanna give it a try.
- The equation is of form f(y) = g*x + s, where f(y) is g*y + a*sinh(b*y).
- We can't analytically find inverted function, but we can compute it for a range, store in array and interpolate - assuming than g,a,b are constant - and they are

- then y = inv_f(g*x+s)

btw. what is the other distortion? it's based on a circuit?

Richard_Synapse · Post by **Richard_Synapse** » Tue Oct 07, 2014 9:31 am

IIRC the Simulanalog method involves the derivative of the input signal. Not sure what implications this has regarding accuracy, but it might be better if you can avoid that.

Richard

Miles1981 · Post by **Miles1981** » Tue Oct 07, 2014 9:47 am

Yes, I made another function based on the SD1 distortion pedal. I'm still in the process of thinking about amps, but I don't have the time at the moment

Richard > it uses the derivative of the signal to analyze the stability of the algorithm. Then the derivative appears due to the trapezoidal integration, but that's OK IMHO.

itoa · Post by **itoa** » Tue Oct 07, 2014 12:25 pm

Any idea on how to make it stable?

y = f*(in-feedback) + s - 0.00016 * sinhf(feedback*40.0)

sinhf acts like 'a switch' and after a threshold quickly approaches to inf. This causes huge numerical problems when using Newton-Rhapson.

Z1202 · Post by **Z1202** » Tue Oct 07, 2014 5:06 pm

itoa wrote:Any idea on how to make it stable?

y = f*(in-feedback) + s - 0.00016 * sinhf(feedback*40.0)

sinhf acts like 'a switch' and after a threshold quickly approaches to inf. This causes huge numerical problems when using Newton-Rhapson.

I thought you wanted to use a table (sorry, I'm following this thread only superficially). How about solving for the value rather than the argument of sinh? (Or for anything containing the value of sinh).

itoa · Post by **itoa** » Tue Oct 07, 2014 5:14 pm

Table works great

but I'm curious on different methods of transforming nonlinear ODEs to something solvable

itoa · Post by **itoa** » Tue Oct 07, 2014 6:14 pm

How about off-current inaccuracy in real diodes? How many % is it?

Miles: could you post ODE of your circuit? I can't figure this out from your code :/

Ivan_C · Post by **Ivan_C** » Tue Oct 07, 2014 7:45 pm

If you use a table with precomputed tables, do you still have any problem ? If not, that means your problem is about the convergence of Newton-Raphson. If you still have instability, then your ODE may be stiff, and there is a numerical way to verify it. But since you use a trapezoidal integrator, stiffness shouldn't be a problem, so I guess it's Newton Raphson. Or a standard algorithm bug

Could you post some pseudo code showing what you are doing ?

itoa · Post by **itoa** » Tue Oct 07, 2014 8:43 pm

Wolfen: I think that diodes make systems stiff as a hell

and thats the main problem.

Using table for inverted function improves stability region greatly. Although the limit still exists its quite acceptable.

camsr · Post by **camsr** » Tue Oct 07, 2014 9:52 pm

Maybe try putting a resistor between the diodes and ground?

Z1202 · Post by **Z1202** » Wed Oct 08, 2014 6:47 am

I think, if you try solving for the value rather than the argument of sinh, then sinh works as a saturator, rather than the booster. That should make the system kind of the opposite of being stiff. At least seems so to me at the first look, maybe I'm wrong here.

Speaking of trapezoidal integration and stiffness. Trapezoidal integration may have a problem with that, particularly in case of strong positive feedback. But I don't think that's the case here.

itoa · Post by **itoa** » Wed Oct 08, 2014 7:03 am

Yes you are right.. reverse function forms a sigmoid and this helps a lot + as this is 1 dimensional equation, this is instantly solvable and fast

btw. Just realised that these RC values means 7MHz cutoff SIC?!

Richard_Synapse · Post by **Richard_Synapse** » Wed Oct 08, 2014 8:48 am

Inverse function is a really clever idea that should work.

Btw, you can also use Bisection method, should be robust and work fine even in realtime (if you don't like tables). You already know the output is never going to exceed a certain value as it's clipped by the diodes, so you can start the iteration at +/- 1V or something.

Richard

itoa · Post by **itoa** » Wed Oct 08, 2014 9:21 am

A bit excitation here. Just found a method of doing this analytically for practically any number of dimensions, this reduces aliasing as well. I mean computation of n-dimensional inverse function. Should I share ?

edit: its a bullshit

except alias reduction part haha

Diode clipper simulation instability