Would this approach be possible (for analog modeling)?

So, I guess this might not be really possible?

My basic idea was just to spot the differences between input and output
after processing and applying them to another signal. The reason why I
thought the signal should gain in volume was that I'd have "difference
spectrums" for every possible input volume. Of course, this might be
tricky to do, but if the CPU power would be enough to do this in realtime,
wouldn't this "different volumes" thing eliminate some of the
"non-linearity" problems?

(I'm not a good mathematican, so please understand if my stuff sounds a
bit silly :) but I was able to program a parametric equalizer, so at least
I understand the basic FFT stuff. But try to avoid answering with
mathematic formulas only :D )

Rock Lobster wrote:
> So, I guess this might not be really possible?

The above discussion was on the use of FFT as analysis tool for non-
linear systems. Modeling non-linear systems is a different story, and
has been done before.

>
> My basic idea was just to spot the differences between input and output
> after processing and applying them to another signal. The reason why I
> thought the signal should gain in volume was that I'd have "difference
> spectrums" for every possible input volume. Of course, this might be
> tricky to do, but if the CPU power would be enough to do this in realtime,
> wouldn't this "different volumes" thing eliminate some of the
> "non-linearity" problems?

Somebody already cooked up (and patented, I believe) an algorithm that
is similar to your ideas:

http://www.sintefex.com/docs/appnotes/dynaconv.PDF

It describes an alternative to the Volterra Series approach for
modeling non-linearities. I don't know how well it works (never heard
it), but Sintefex is using the algorithm in their pro-audio "vintage
gear modelling" units (a guitar amp can also be described as "vintage
gear" in these days of virtual guitars :-), and just received an award
for their technology (details on their website).

>
> (I'm not a good mathematican, so please understand if my stuff sounds a
> bit silly :) but I was able to program a parametric equalizer, so at least
> I understand the basic FFT stuff. But try to avoid answering with
> mathematic formulas only :D )

The level of maths in that article doesn't exceed the usual
convolution sums. The idea is to interpolate different filters,
depending on the level of the input signal.

Regards,
Andor

Hi,

I may have a good answer, although I'm not sure if it still fits your
question anymore...

Using FFT to get a simple frequency response is a standard technique.
Divide FFT(out) by FFT(in) sample-by-sample (complex), and you'll get the
complex frequency response. IFFT gives you the impulse response, plug that
into a convolutional reverb and you'll get exactly the undistorted amp
sound (probaby with a huge delay but still).

But you seem to be after a model for the amplifier nonlinearity. 
That works even without FFT:

- Create a suitable test signal, record some low and high notes. The
better the statistics of your model match what's later encountered during
operation, the more accurate the model (in a least-squares sense).

- Play the signal, record the output, oversample as needed, time-align
input and output signal. Alignment accuracy is most critical.
- Build a set of base vectors [1; x; x^2; x^3; x^4; ...] where x is your
input signal
- Use the backslash operator in matlab to decompose your recorded signal
into the base vectors, least-squares sense. If you get warnings about
rank, use less terms.
- the result vector gives the polynomial coefficients for your amplifier
nonlinearity. Double precision arithmetics may allow using for example up
to 17th order.

- Evaluate the polynomial at 100 different points, straight line
interpolation in-between works OK. That's the model of your amplifier
nonlinearity.

If you want to take frequency response into account, include delayed
signals as your base vectors. This already goes towards simple Volterra
series modeling.

I've been wondering for a while whether this works for guitar, but it sure
does work for radio frequency amplifiers. I use this frequently in the lab,
a two-tap model usually leaves about 1/10000 of the received signal power
unexplained (-40 dBc).

If interested, search for AMAM/AMPM model for power amplifiers on the web.
The difference is that you use only real numbers, so there is no AMPM, and
your polynomial coefficients are real valued.
The method works for weakly nonlinear systems, you may be out of luck with
fuzz or heavy sounds

Cheers

Markus

PS: I might post some example code on a dsprelated.com blog in a while
(assuming it actually works with audio amps). Stay tuned...