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.