Re: Convolution for Laplace Transform
- From: spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci)
- Date: Tue, 2 Dec 2008 14:01:14 +0100 (CET)
In article <7b483a16-6af4-47e7-a3bf-5b0030c4a9f5@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
pcoords29@xxxxxxxxx writes:
Hello,
If I know only the function values of f(t) & g(t) for various t, how
do I go about finding the convolution, f(t) * g(t) for each value
of t?
I don't know how to integrate f(u) g(t-u) du between 0 and t , as f
and g are not known explicitly.
Any help is most appreciated.
Thanks.
Sid
as far as concerns this text, no Laplace transform is involved if not
integral{f(u)*g(t-u)}du should serve as the inverse Laplace for F(s)*G(s).
well, concerning your integration problem:
if the data for f and g are available on the same grid, then
you could use composed Newton-Cotes rules directly.
or, maybe better (depends on the precision of your function values:
are these data with some (if only little) noise??)
interpolate the data for the two functions by piecewise polynomials independently,
for example cubic splines, but using the same grid, then
after rsubstituting the varaibles multiply the spline pieces
getting a piecewise polynomial of higher order (6 for the cubic) in u
and integrate this in turn piecewise using an appropriate Gauss rule.
this of course for grid of t-values, and finally interpolate this data
again by a spline.
should work without trouble
hth
peter
.
- References:
- Convolution for Laplace Transform
- From: pcoords29
- Convolution for Laplace Transform
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