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Nonlinear System Identification

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Nov 28, 2005
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system identification with volterra series matlab

Hi everyone

Is there anyone who know sth about how to find the transfer function of a nonlinear system(valve amplifier)?

As I know that if it's a linear system, we will just input a white noise as random as possible... Will this apply to nonlinear system?

I am thinking about using matlab to play a wave file as input and record the output of the nonlinear system to get the transfer function... Can anyone give me some tips/clues?



If you want to identify a nonlinear system use nonlinear models, otherwise you get only linearized about one point model. As a modelling tools you can use recurrent neural networks, time delayed neural networks or fuzzy systems. It is very hard to infer nonlinear system equations if you know nothing about the system, it can be aproximated by nonlinear models ( eg. NARMA ).

Thanks for your treasurable advices..
Is there any software can help me to complete this task?

tobby said:
Thanks for your treasurable advices..
Is there any software can help me to complete this task?

There's a System Identification Toolbox in MATLAB.

Smooth nonlinearities (like in your case) can be modelled by Volterra series

You can see:

1. Identification using sweep sine
A. Farina, A. Bellini, E. Armelloni, Non-Linear
Convolution: A New Approach For The Auralization Of Distorting Systems, Proceedings
of the 110th AES Convention, 2001 May 12-15 Amsterdam, The Netherlands

2. Identification using MLS
MJ Reed and MOJ Hawksford. Identification of discrete Volterra series
using maximum length sequences. IEE Proc.-Circuits Devices Syst., 143(5):241-248,
October 1996.

For details on identification and modelling you can see book
VJ Mathews and GL.Sicuranza, Polynomial Signal Processing, New
York: John Wiley & Sons, Inc., 2000.


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Aurora 4 plugin for Adobe Audition 1.5

thanks for your advice!
the AES paper helps me a lot, but, indeed, i don't know how to use the Aurora 4 plugin for Adobe Audition 1.5..

Unfortunately, I do not work with Audition...

Fll calculation I made in Matlab, or in CoolEdit.

The idea is simple, and Matlab code becomes not so long.

tobby said:
Is there anyone who know sth about how to find the transfer function of a nonlinear system(valve amplifier)?


From what i know for a system to have transfer function the necessary condition is that this system is both linear and time invariant.
Transfer function do not fully describe the properties of a system (you may loose subsystems that are not controllable and/or not observable).
That's why it is better to use state equations so that you do not loose information about the sys.
Off course for state equations to exist the system has to be casual (realizable).Therefore for systems that are nonlinear and/or time time variant you have to use state equations for analysis.

Neural Network

Do anyone think that using neural network is better than Volterra series for nonlinear audio system modelling?

the major ways of solving your problem are the following:
- nonlinear identification (see Lee-Schetzen the volterra and wiener theories)
- fixed point equalization (nowak)
- Minimize the mean square error |y_est - y|^2
- polynomial method, try to form a polynomial and seek for its roots
- adaptive filters
- Identification using orthogonal functions
- Least squares approach
- Neural network approach


The Volterra Series requires a ruge computation. I Like to use NARMAX or NARX models. They use least square modified to estimate the coeficients. I can send to you the equations of those models.


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