Re: inverse laplace transform

Bhaskar Thiagarajan wrote:

"Tim Wescott" <tim@xxxxxxxxxxxxxxxx> wrote in message
news:wYGdnbPA6obFKjTe4p2dnA@xxxxxxxxxxxxxxx

Bhaskar Thiagarajan wrote:

Hi all

I'm working on trying to model a non-linear system (described by a 

second

order differential eqn) into a discrete IIR filter. 

Whoa!  Stop right there!

The Laplace transform (and the z transform) only work with linear
systems.  You simply cannot do a Laplace transform of a nonlinear
system: it doesn't work.  You can dink with Volterra series and all that
fun stuff, but then you're not really doing a Laplace any more.



Hmm...I think I mis-spoke. My instinct tells me that a second order
differential equation is non-linear. However, I just looked up the Rick
Lyons' book and I see that he calls it a linear system. I'm just going to
take his word for it for now and revisit it later.

You can have an any-order (up to infinite) differential equation that is linear. The order of the diff. eq and it's linearity are orthogonal properties.

You may want to do a bit of digging and remind yourself of the properties of linearity and time-invariance (they are two different properties). The Laplace transform only works on systems that are linear and time invariant. The z transform only works on systems that are linear and who's time variance is cyclical at the reference rate.

If you're clever and determined you can use Fourier analysis on some systems that are time varying, like systems with sampling and superheterodyne radio receivers.

--

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

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