Nonlinear system

In case of linear time invariant systems we can use convolution to
represent the system or to find the system response. However if we have a
nonlinear system how can we find the system response or the transfer
function of the system? any ideas?
		
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aries44 wrote:

> In case of linear time invariant systems we can use convolution to
> represent the system or to find the system response. However if we have a
> nonlinear system how can we find the system response or the transfer
> function of the system? any ideas?
> 		
> This message was sent using the Comp.DSP web interface on
> www.DSPRelated.com

Both the notion of a general system response and of a transfer function 
are not generally valid for nonlinear systems.  For a system with a 
"mild" nonlinearity you can approximate it's response by linearizing and 
finding the transfer function, then being careful how you use the 
result.  For a system with a "severe" nonlinearity you have to throw 
away the linear analysis entirely and start using heavy math.

It is not uncommon with nonlinear systems to use a combination of 
heavily simplified system models for theoretical calculations combined 
with carefully constructed simulations to speed up system design.

The difference between "mild" and "severe" depends on interpretation. 
Indeed, you will often find it useful to call a system linear for one 
set of circumstances, and nonlinear for another.  When I am analyzing 
control systems I'll often use linear analysis for finding the best 
controller for small disturbances and command inputs, but I'll use 
nonlinear analysis and synthesis techniques to insure that the system is 
unconditionally stable and will respond appropriately to large 
disturbances and/or control inputs.

-- 
-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

aries44 wrote:
> In case of linear time invariant systems we can use convolution to
> represent the system or to find the system response. However if we have a
> nonlinear system how can we find the system response or the transfer
> function of the system? any ideas?

I suggest you Google on "Volterra series".  Difficult 
problem.  Expensive solutions (measurement and computation.)

A good intro is here:

http://tinyurl.com/dqo54

In long form:

http://lanoswww.epfl.ch/studinfo/courses/cours_nonlinear_de/extras/Cherry(1994)_Distortion%20Analysis%20of%20Weakly%20Nonlinear%20Filters%20Using%20Volterra%20Series_Chap3.pdf

There isn't generally "a" transfer function because it 
depends on the levels (also in a frequency dependant way.)


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Here is an approach on how you could model non-linear systems using
impulse responses:

http://www.sintefex.com/docs/a=ADppnotes/dynaconv.PDF=20

Regards,
Andor

A Volterra series. Wiener first worked this out in the 1930s called the
Wiener Expansion and J.F.Barrett did the work independantly. It is a
sort of series of convolution integrals.