🚀 go-pugleaf

In article <1d3fv0INNfo3@usenet.INS.CWRU.Edu> at913@cleveland.Freenet.Edu (Mirko Vukovic) writes:

>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?


>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):

			....................

This does not do the job, and in fact it is not clear how it can be done.

The idea of the FFT is that one can use the n/k FTs for the points spaced
k apart, and manipulate properties of the FT for k equally spaced points, to
get the FFT for n equally spaced points.  One also increases the number of
points at which it is calculated, which is the same as the number of points
in the argument.  Nothing like this is possible for the Laplace transform
UNLESS additonal sample points are interpolated.  

Another indication of the problem is that inverting a Fourier series is 
easy, but inverting a Laplace transform, while it can be done, in principle,
without using complex arguments, is likely to be very difficult to do in
practice that way.  The two transforms are not that similar
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
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