Re: [music-dsp] Simulating Valve Amps
[Andrew Simper] On 18 June 2014 21:01, Tim Goetze t...@quitte.de wrote: I absolutely agree that this looks to be the most promising approach in terms of realism. However, the last time I looked into this, the computational cost seemed a good deal too high for a realtime implementation sharing a CPU with other tasks. But perhaps I'll need to evaluate it again? The computational costs of processing the filters isn't high at all, just like with DF1 you can compute some simplified coefficients and then call process using those. Since everything is linear you end up with a bunch of additions and multiplies just like you do in a DF1, but the energy in your capacitors is preserved when you change coefficients just like it is when you change the knobs on a circuit. Yeh's work on the Fender tonestack is just that: symbolic nodal analysis leading to an equivalent linear digital filter. I mistakenly thought you were proposing nodal analysis including also the nonlinear aspects of the circuit including valves and output transformer (which without being too familiar with the method I believe to lead to a system of equations that's a lot more complicated to solve). -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Simulating Valve Amps
On 20.06.2014, at 11:11, Tim Goetze t...@quitte.de wrote:
I
mistakenly thought you were proposing nodal analysis including also
the nonlinear aspects of the circuit including valves and output
transformer (which without being too familiar with the method I
believe to lead to a system of equations that's a lot more complicated
to solve).
Well, it might not be as straight forward, but there are various methods to
solve non-linear systems of equations.
The main problem arises when a non-linear element occurrs on both sides of an
equation, such as
Vout = g * ( tanh( Vin ) - tanh( Vout ) ) + iceq
As one can't solve this for Vout, there's a few different approaches to deal
with it computationally.
The most common one is to introduce a unit delay (aka the naive method)
Vout[ n ] = g * ( tanh( Vin[ n ] ) - tanh( Vout[ n - 1 ] ) ) + iceq
This however leads to mangled phase/frequency response and worse time invariant
properties, e.g. when sweeping g
A quick and easy method to resolve this is to only apply the unit delay to the
effect of the non-linearity itself, but keep the system delay-less for its
linear components:
Vout = g * ( tanh( Vin ) - f[ n-1 ] * Vout ) + iceq
f[ n ] = tanh( Vout )/Vout;
This way the equation can be solved for Vout and the non-linearity becomes a
factor that's applied with one sample delay.
Similar methods apply an offset and a tangent to linearize the non-linearity
for a moment in time.
So far this is computationally easy going, but it's also a compromise in
accuracy. To become numerically accurate one typically uses iterative methods
to look into the future. A very simple approach is to estimate the value in
question, calculate the equation and compare the estimate with the result. From
there on one can refine the estimate until it converges with the result in any
desired accuracy, such as
while ( abs( Vout_result - Vout_estimate ) 0.0001 )
{
Vout_estimate = rootFindingAlgorithmOfChoice( Vout_result );
Vout_result = g * ( tanh( Vin ) - tanh( Vout_estimate ) ) + iceq
}
There you go. It's very basic and it can be optimised to run on a modern CPU.
Cheers,
- Urs
--
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Re: [music-dsp] Simulating Valve Amps
On 20 June 2014 17:11, Tim Goetze t...@quitte.de wrote: [Andrew Simper] On 18 June 2014 21:01, Tim Goetze t...@quitte.de wrote: I absolutely agree that this looks to be the most promising approach in terms of realism. However, the last time I looked into this, the computational cost seemed a good deal too high for a realtime implementation sharing a CPU with other tasks. But perhaps I'll need to evaluate it again? The computational costs of processing the filters isn't high at all, just like with DF1 you can compute some simplified coefficients and then call process using those. Since everything is linear you end up with a bunch of additions and multiplies just like you do in a DF1, but the energy in your capacitors is preserved when you change coefficients just like it is when you change the knobs on a circuit. Yeh's work on the Fender tonestack is just that: symbolic nodal analysis leading to an equivalent linear digital filter. I mistakenly thought you were proposing nodal analysis including also the nonlinear aspects of the circuit including valves and output transformer (which without being too familiar with the method I believe to lead to a system of equations that's a lot more complicated to solve). Nodal analysis can refer to linear or non-linear, so sorry for the confusion. I was trying to point out that the linear analysis done by Yeh starts the circuit but then throws it away and instead uses a DF1, and a DF1 does not store the state of each capacitor individually, so when you turn the knob you don't get the right time varying behaviour. I am saying you don't have to throw the circuit away, you can still get an efficient implementation since in the linear case everything reduces to a bunch of adds and multiplies. For non-linear modelling you need additional steps, and depending on the circuit there are many different methods that can be tried to find the best fit for the particular requirements. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Simulating Valve Amps
On 6/20/14 10:57 AM, Andrew Simper wrote: On 20 June 2014 17:11, Tim Goetzet...@quitte.de wrote: [Andrew Simper] On 18 June 2014 21:01, Tim Goetzet...@quitte.de wrote: I absolutely agree that this looks to be the most promising approach in terms of realism. However, the last time I looked into this, the computational cost seemed a good deal too high for a realtime implementation sharing a CPU with other tasks. But perhaps I'll need to evaluate it again? The computational costs of processing the filters isn't high at all, just like with DF1 you can compute some simplified coefficients and then call process using those. Since everything is linear you end up with a bunch of additions and multiplies just like you do in a DF1, but the energy in your capacitors is preserved when you change coefficients just like it is when you change the knobs on a circuit. Yeh's work on the Fender tonestack is just that: symbolic nodal analysis leading to an equivalent linear digital filter. I mistakenly thought you were proposing nodal analysis including also the nonlinear aspects of the circuit including valves and output transformer (which without being too familiar with the method I believe to lead to a system of equations that's a lot more complicated to solve). Nodal analysis can refer to linear or non-linear, so sorry for the confusion. well, Kirchoff's laws apply to either linear or non-linear. but the methods we know as node-voltage (what i prefer) or loop-current do *not* work with non-linear. these circuits (that we apply the node-voltage method to) have dependent or independent voltage or current sources and impedances between the nodes. I was trying to point out that the linear analysis done by Yeh starts the circuit but then throws it away and instead uses a DF1, and a DF1 does not store the state of each capacitor individually, so when you turn the knob you don't get the right time varying behaviour. in the steady-state (say, a second after the knob is turned) is there the right behavior with the DF1? I am saying you don't have to throw the circuit away, you can still get an efficient implementation since in the linear case everything reduces to a bunch of adds and multiplies. and delay states. For non-linear modelling you need additional steps, and depending on the circuit there are many different methods that can be tried to find the best fit for the particular requirements if, the sample rate is high enough (and it *should* be pretty fast because of the aliasing issue) the deltaT used in forward differences or backward differences (or predictor-corrector) or whatever should be pretty small. in my opinion, if you have a bunch of memoryless non-linear elements connected in a circuit with linear elements (with or without memory), it seems to me that the simple Euler's forward method (like we learned in undergraduate school) suffices to model it. Andrew, i realize that you had been using something like that to emulate linear circuits with capacitors and resistors and op-amps. it does make a difference in time-variant situations, but for the steady state (a second or two after the knob is twisted), i'm a little dubious of what difference it makes. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
[music-dsp] Breakthrough in mastering.
Heya. I have a new blog up, and as some of you know, I have been working on DSP for a while, and my products are linked there, along with my music. I feel that I have made a breakthrough in mastering, and would like to share it with you. Introducing also The Karlsen Window, that is a minimal-phase gaussian filter, with the rise (fastest half) mirrored (and 1 sample truncated on each side, in mine.) Featured as an option in my limiter linked on that page. And I am also working on a compressor, with selectable overshoot, and a gaussian filter, that makes very well use of the limiter. The result is very musical. https://www.youtube.com/watch?v=s4KvJj9x6Xk A bit more on the blog about the compressor aswell. Best Regards, Ove Karlsen Artists, researcher, engineer Monotheo.biz -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
