Re: mathematica doesn't find periodic response with laplace transform

*To*: mathgroup at smc.vnet.net*Subject*: [mg106977] Re: mathematica doesn't find periodic response with laplace transform*From*: Noqsi <jpd at noqsi.com>*Date*: Sat, 30 Jan 2010 07:12:15 -0500 (EST)*References*: <hjp7ot$d69$1@smc.vnet.net>

On Jan 27, 4:24 am, nukeymusic <nukeymu... at gmail.com> wrote: > In every course on Laplace transforms you'll find that the Laplace > transform of a periodic signal with period tee is found by multiplying > the Laplace transform of one period by 1/(1-Exp[-tee*s]). That factor > replaces the series expansion 1 + Exp[-tee*s] + Exp[-2*tee*s] + Exp > [-3*tee*s]+ ... > Unfortunately Mathematica doesn't seem to work according to this. > As an example I have taken a square wave with amplitude 3V and period > tee which is applied to a low pass filter with time constant tau. > You'll see that Mathematica doesn't calculate the correct response > using the above mentioned factor. > As a workaround and also to show what the correct result should be > (for three periods) I also calculated the response by multiplying by > (1 + Exp[-tee*s] + Exp[-2*tee*s] + Exp[-3*tee*s]) > Here is my code: > hs = 1/(1 + tau*s) > hps = 1/(1 - Exp[-tee*s]) > h1Ts = Exp[-tee*s] > tau = 33.0*^-6 > tee = 330.0*^-6 > ui1t = 3*HeavisideTheta[t] > ui2t = -6*HeavisideTheta[t - tee/2] > ui3t = 1 - HeavisideTheta[t - tee] > uit1 = (ui1t + ui2t)*ui3t > Plot[uit1, {t, 0, 1500*^-6}] > uis = LaplaceTransform[uit1, t, s] > uisT = uis*(1 + Exp[-tee*s] + Exp[-2*tee*s] + Exp[-3*tee*s]) > uisTbis = uis*hps > uitT = InverseLaplaceTransform[uisT, s, t] > uitTbis = InverseLaplaceTransform[uisTbis, s, t] > Plot[uitT, {t, 0, 1500*^-6}] > Plot[uitTbis, {t, 0, 1500*^-6}] > uos = uisT*hs > uot = InverseLaplaceTransform[uos, s, t] > Plot[uot, {t, 0, 1500*^-6}] > > does anybody here a way to make Mathematica act correctly for this > case? So, your complaint seems to be that Mathematica returned InverseLaplaceTransform[uisTbis, s, t] unevaluated. It would have been helpful if you'd said that. What did you expect it to do? Note that few functions have closed form inverse Laplace transforms.