🚀 go-pugleaf

In a previous article, fang@phy.duke.edu (Fang Zhong) says:

>
>	We are studying a decaying time series.  We would like
>to have a Laplace Transform of our experimental data, so we can
>analyze all the exponential decaying modes.  Is there anything
>in numerical analysis that does the forward LT, just like FFT
>to help analyzing data in frequency demain?
>
>-- 
>	Fang Zhong				1-919-660-2524
>	Duke University Dept. of Physics	fang@phy.duke.edu
>	Durham, N.C.      27706			
>

OK, here is an extremely hazy suggestion  (I don't have any signal processing
books for firm definitions etc.)

LT is a generalization of FT to the whole complex plane, where FT is the LT on
the unit circle.

If you multiply your time series by alpha^t (I think), the LT of the new
series expands or contracts by the factor alpha (lookup Oppenheim's book
on descretem time signal analysis):

	f(t) <--> F(s)

f(t)*alpha^t <--> F(alpha*s)

So, you can modify your time series in the above way, to bring the appropriate
circles of the complex plane to the unit circle, and then you use the FFT.

Mind you, this is my (highly original :-)) contribution to science, meaning
that I've never seen it anywhere else, nor have seen (or looked) for an 
alternative way of doing a FLT.  FUrther more, I've never tried it, only 
thought about it.  Enough disclamers.

-- 
Mirko Vukovic 
University of Wisconsin -- Madison
VUKOVIC@UWMFE.NEEP.WISC.EDU