This is very interesting. Although i must confess that i have no idea how to model your feedback loop in Pd. As for the lp filter, i have never used an upsampled filter. Is it enough if i use the filter built in Miller's J07 Upsampling example? It's a 3rd order butterworth lp and the subpatch is upsampled 16 times. More generally, what is the best way to split a signal into low and high frequencies? I thought of using fft, with, say, a gain equal to 1 for frequencies between 0 and X Hz, and equal to 0 above. Would this work? This would be the sharpest lp filter, wouldn't it?
Pierre
2010/10/14 - fallen_devil@gmx.de
Am 12.09.2010 19:24, schrieb Martin Peach:
On 2010-09-12 12:05, Mathieu Bouchard wrote:
On Sun, 12 Sep 2010, Martin Peach wrote:
It's not the capacitors, it's the amplifier losing gain when it approaches the power supply.
Yeah, but it seems to be a pattern similar to the one found in capacitors, because capacitor theory has exp(-x) all over it, and the only way that capacitors behave like [hip~] is when the signal is much below the capacity rating (?F)... otherwise they lose gain... when they don't, it's because exp(-x) can be well approximated by x.
I guess it's similar since capacitors charge at a rate proportional to a voltage difference, while transistors can supply charge carriers at a rate proportional to a voltage difference, so caps charge fastest when they are nearly empty and transistors have the best gain with small signal inputs.
The whole universe has exp written all over it in fact...
And then, exp is very close to tanh in several different ways, one of them being this (use gnuplot) :
plot [-2:2] [-1:1] exp(x*sqrt(2))-1, 1-exp(-x*sqrt(2)), tanh(x), x
I put the plain 'x' at the end to show what I mean above (though you already know that)
Of course, all the hyperbolic trig functions are made from exp, by definition.
http://en.wikipedia.org/wiki/Hyperbolic_function
Another use of exp is the sigmoid function used in biology, that can be used to make a soft transition from one state to another as in 'fuzzy logic'.
Martin
Sorry I don't know (jet) how to answer a mail from the archives.
The soft clipping in a normal analogue guitar distortion (like the tube screamer) comes from the diodes (tubes are warmer). Which have log written over them (their resistance depending on V). (Are even used some time as a simple analogue log function)
A analogue guitar distortion is build via a feedback loop like this:
|--var resistor (gain) |---- ->diode -| |---- <-diode -| |----cap as lp -| | | |------ (-) | op-amp---|---out input-- (+)
The resistor defines the max gain The cap is used as a lp (short cuts high frequency's to a gain of 1)
An op-amp tries to have always the same voltage at both inlets. Which means if you have 1v at + it increases its output till you have 1v at - as well. 1+(-1)==0
And finally the diodes: At negative voltages they blockade completely At low voltages they have a high resistance so the gain of the resistor counts. At around .7V their resistance drops leading to a lower gain.
With a tanh(sig) you are simulating the diodes in a simple way. What usually is forgotten in the digital domain is the lp filtering. You may want to split your signal into a high and low part. Run the low part through the tanh and sum it later up with the high part.
It gets really funny if you want to try to model the whole feedback loop in something like pd. There is a mess of phase changes and whatnot which surely is part of the interesting analogue sound.
An important thing to mention is that, as someone else noted, you need to (should) oversample to avoid aliasing with high order functions. Tanh is one of the worst because it generates very high harmonics. Where in the analogue field a natural lp filtering happens all the time (and no aliasing can occur). As an Example: An opamp has a frequency response up to GHz. But only at a gain of 1. The higher the gain the lower the frequency response.
I'm bad at explaining things. But if you want to i can search my bookmarks for the analogue or digital sources i tried to explain here.
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