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.
> 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?
> 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
Reply by aries44●June 27, 20052005-06-27
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