[music-dsp] testsignals for nonlinear system identification

[pickman at inwind.it]

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
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>From      : music-dsp-bounces at music.columbia.edu
To          : "A discussion list for music-related DSP" music-dsp at music.columbia.edu
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 at mur.at
> Date: Tue, 29 Apr 2008 08:06:02 -0700
> To: A discussion list for music-related DSP music-dsp at music.columbia.edu
> 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
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