       Problem with LaplaceTransform (Help !)

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg949] Problem with LaplaceTransform (Help !)
• From: gottsch at mikro.ee.tu-berlin.de (Gert Gottschalk)
• Date: 27 Apr 1995 22:13:45 GMT
• Organization: Technical University Berlin, Germany

```
Hello,

I am looking into filter behaviour in signal processing. To do so
I make use of LaplaceTransform and InverseLaplaceTransform.
When I want results to be evaluated as in Plots I get problems
from the transform with numerical computation error messages and
warnings.

I define:

In:= <<Calculus`LaplaceTransform`
In:= om[t_]:= If[t>0,1,0]
In:= q[s_] := LaplaceTransform[om[t],t,s]
In:= Plot[q[s],{s,0,100}]

And get :
1
Power::infy: Infinite expression -- encountered.
0.

1
Power::infy: Infinite expression -- encountered.
0.

1
Power::infy: Infinite expression -- encountered.
0.

General::stop: Further output of Power::infy
will be suppressed during this calculation.

NIntegrate::precw:
Warning: The precision of the argument function (
Exp[-(0. t)] If[t > 0, 1.1, 1]) is less than WorkingPrecision (16).

NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one of the following:
singularity, oscillatory integrand, or insufficient WorkingPrecision.

NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after 7
56
recursive bisections in t near t = 2.28833 10  .

NIntegrate::precw:
Warning: The precision of the argument function (
Exp[-(0. t)] If[t > 0, 1.1, 1]) is less than WorkingPrecision (16).

NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one of the following:
singularity, oscillatory integrand, or insufficient WorkingPrecision.

NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after 7
56
recursive bisections in t near t = 2.28833 10  .

Plot::plnr: CompiledFunction[{s}, q[s], -CompiledCode-][s]
is not a machine-size real number at s = 0..

General::ovfl: Overflow occurred in computation.

General::ovfl: Overflow occurred in computation.

General::ovfl: Overflow occurred in computation.

General::stop: Further output of General::ovfl
will be suppressed during this calculation.

The plot I finally get doesn't look like what I expected
a simple switch in frequency.

I think the problem comes from the integration in the transform.
Normally it is done from -infinity to +infinity. With a finite
set of data I would like to reduce this range.
Perhaps then also the result of the transform would become better

Gert Gottschalk

gottsch at mikro.ee.tu-berlin.de

TU-Berlin Institute for Microelectronics   |    Yesterday reality ceased to exist,
Sekr. J-13, Jebensstr. 1, D-10623 Berlin   |    All you're experiencing now is the
Germany         Tel.(+4930)-31426704       |    sole product of your imagination.
FAX (+4930)-31424597       |                    G.G.G.

```

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