testsignals for nonlinear system identification

[Georg Holzmann-2]

Hallo!

I am searching for good testsignals to identify nonlinear audio systems
(like tubes, distorsion effects, ...) with volterra/wiener systems and
neural networks.
So far I tried bursts of noise and also bursts of sines, but they don't
always work as I want when using the identified system afterwards with
general audio signals ...

I have found the following DAFX papers about that topic:
"A Measurement Technique for Highly Nonlinear Transfer Functions"
(Möller, Gromowski, Zölzer)
and
"Discrete-Time Models for Nonlinear Audio Systems"
(Schattschneider, Zölzer)
where they used noise and sine bursts.

Are there any other resources which signals to use for nonlinear system
identification or does anyone want to share some practical knowledge ?

Many thanks for any hints,
LG
Georg
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[Charles Henry]

On Tue, Apr 29, 2008 at 11:05 AM, Georg Holzmann <grh@...> wrote:
>  Are there any other resources which signals to use for nonlinear system
> identification or does anyone want to share some practical knowledge ?
>
>  Many thanks for any hints,
>  LG
>  Georg

That sounds like an interesting problem.  I don't have much to
suggest, but this is a hint.  Passive non-linearities will generate
difference tones.  So, a test signal with frequencies f1 and f2 will
create difference tones with frequencies |f1-f2| and others.

It seems like non-linearities acting on noise would be hard to
decipher after the fact, but a signal with just a few frequencies
would create some very clear effects related to the transfer function.

Chuck
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[Bogac Topaktas]

Hi Georg,

In the following paper, Dr. Jonathan S. Abel and Dr. David P. Berners of Universal Audio
describe a method for identifying the parameters of a Volterra system:

J. S. Abel and D. P. Berners, "A technique for nonlinear
system measurement," in Proc. 121st AES Convention,
San Francisco, CA, Oct. 2006.
http://www.aes.org/e-lib/browse.cfm?elib=13785

A comprehensive resource on the subject is:

Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models
by Oliver Nelles
Springer; 1 edition (December 12, 2000)
ISBN-10: 3540673695 ISBN-13: 978-3540673699

> Are there any other resources which signals to use for nonlinear system
> identification or does anyone want to share some practical knowledge ?

There is a commercial product called "Nebula" from Acusticaudio which
partially mentions "Volterra" in its title:

http://www.acusticaudio.net/

Apparently, it includes an automated identification tool which is called NAT. You can
take a look at it (or its documentation) to learn about its test signals and methodology.

Bogac.


-----Original message-----
From: Georg Holzmann grh@...
Date: Tue, 29 Apr 2008 08:06:02 -0700
To: A discussion list for music-related DSP music-dsp@...
Subject: [music-dsp] testsignals for nonlinear system identification

> Hallo!
>
> I am searching for good testsignals to identify nonlinear audio systems
> (like tubes, distorsion effects, ...) with volterra/wiener systems and
> neural networks.
> So far I tried bursts of noise and also bursts of sines, but they don't
> always work as I want when using the identified system afterwards with
> general audio signals ...
>
> I have found the following DAFX papers about that topic:
> "A Measurement Technique for Highly Nonlinear Transfer Functions"
> (Möller, Gromowski, Zölzer)
> and
> "Discrete-Time Models for Nonlinear Audio Systems"
> (Schattschneider, Zölzer)
> where they used noise and sine bursts.
>
> Are there any other resources which signals to use for nonlinear system
> identification or does anyone want to share some practical knowledge ?
>
> Many thanks for any hints,
> LG
> Georg
> --
> 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

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This is what I can say to you.
1)You can use a Volterra system only to reproduce mild non linearities. If u have a system with sharp saturation don't lose your time with Volterra systems.
For example in a dynamic system you have a relation like
dx/dt=f1(x,u)
y=f2(x,u)
so if u cannot approximate f1 with a polynomial expansion a Volterra system will not work.
2)If u have an inside knowledge of your system u can "simply" apply the math to derive the volterra expansion as described in classic texts about Volterra\Wiener systems.
Leo
---------- Initial Header -----------

>From      : music-dsp-bounces@...
To          : "A discussion list for music-related DSP" music-dsp@...
Cc          :
Date      : Tue, 29 Apr 2008 11:58:47 -0700
Subject : Re: [music-dsp] testsignals for nonlinear system identification

> Hi Georg,
>
> In the following paper, Dr. Jonathan S. Abel and Dr. David P. Berners of Universal Audio
> describe a method for identifying the parameters of a Volterra system:
>
> J. S. Abel and D. P. Berners, "A technique for nonlinear
> system measurement," in Proc. 121st AES Convention,
> San Francisco, CA, Oct. 2006.
> http://www.aes.org/e-lib/browse.cfm?elib=13785
>
> A comprehensive resource on the subject is:
>
> Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models
> by Oliver Nelles
> Springer; 1 edition (December 12, 2000)
> ISBN-10: 3540673695 ISBN-13: 978-3540673699
>
> > Are there any other resources which signals to use for nonlinear system
> > identification or does anyone want to share some practical knowledge ?
>
> There is a commercial product called "Nebula" from Acusticaudio which
> partially mentions "Volterra" in its title:
>
> http://www.acusticaudio.net/
>
> Apparently, it includes an automated identification tool which is called NAT. You can
> take a look at it (or its documentation) to learn about its test signals and methodology.
>
> Bogac.
>
>
> -----Original message-----
> From: Georg Holzmann grh@...
> Date: Tue, 29 Apr 2008 08:06:02 -0700
> To: A discussion list for music-related DSP music-dsp@...
> Subject: [music-dsp] testsignals for nonlinear system identification
>
> > Hallo!
> >
> > I am searching for good testsignals to identify nonlinear audio systems
> > (like tubes, distorsion effects, ...) with volterra/wiener systems and
> > neural networks.
> > So far I tried bursts of noise and also bursts of sines, but they don't
> > always work as I want when using the identified system afterwards with
> > general audio signals ...
> >
> > I have found the following DAFX papers about that topic:
> > "A Measurement Technique for Highly Nonlinear Transfer Functions"
> > (M?ller, Gromowski, Z?lzer)
> > and
> > "Discrete-Time Models for Nonlinear Audio Systems"
> > (Schattschneider, Z?lzer)
> > where they used noise and sine bursts.
> >
> > Are there any other resources which signals to use for nonlinear system
> > identification or does anyone want to share some practical knowledge ?
> >
> > Many thanks for any hints,
> > LG
> > Georg
> > --
> > 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
> --
> 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
>

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[Georg Holzmann-2]

Hallo!

First thanks for all the hints - I will go through them !

pickman@... schrieb:
> This is what I can say to you.
> 1)You can use a Volterra system only to reproduce mild non linearities. If u have a system with sharp saturation don't lose your time with Volterra systems.

My question was not meant to be about Volterra Systems. Actually I am
comparing a special neural network architecture (echo state networks) to
standard Volterra Identification and Time Delayed Neural Networks for
nonlinear black-box modeling.
Therefore the test signals should be quite general, so that they can be
used with all those systems ...

Thanks,
LG
Georg
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