🚀 go-pugleaf

In article <6601@news.duke.edu>, fang@phy.duke.edu (Fang Zhong) writes:
|> 
|> 	After informed by a netter, I want to make clearer on my
|> earlier post.
|> 	Yes, we want the time constants in the sum of exponentials,
|> it is basically "relaxation spectrum" analysis as analogous to FFT
|> in "frequency spectrum".
|> 	We tried to use nonlinear fit of multiple exponentials to
|> fit our data, the results were not very good.  So we thought about
|> the Laplace Transform.
|> 	As I was informed, people studying NMR relaxation prcesses
|> already developed certain technique for the analysis.
|> 	Is it available from any ftp site?
|> 	Is there a FLT as to FFT?
|> 	Thanks in advance for helps.
|> 
|> -- 
|> 	Fang Zhong				1-919-660-2524
|> 	Duke University Dept. of Physics	fang@phy.duke.edu
|> 	Durham, N.C.      27706			

I don't know anything about the NMR-related algorithms (although you might
want to follow the thread on Nonlinear Least-Squares on this board), however,
the same problem crops up elsewhere, in system identification, etc. One old
reference is Chapter 11 of "Digital Spectral Analysis", by S. Marple. This
chapter is concerned with "Prony's Method" - fitting damped sinusoids to
a time series. The book includes a Fortran program. As I recall, the method
works well with low-noise data, but as S/N decreases, a big problem is
determining the number of sinusoids present. 


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Besides NMR relaxation measurements what other areas need 
numerical inverse Laplace Transforms?

Keith S Cover
Physics, UBC
Vancouver, B.C.
Canada
keith@msmri.med.ubc.ca