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MathGroup Archive 1995

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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[1]:= <<Calculus`LaplaceTransform`
In[2]:= om[t_]:= If[t>0,1,0]
In[3]:= q[s_] := LaplaceTransform[om[t],t,s]
In[4]:= 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

I would like to hear comments about these thoughts.

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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