Re: convolution involving UnitStep

*To*: mathgroup at smc.vnet.net*Subject*: [mg126142] Re: convolution involving UnitStep*From*: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>*Date*: Fri, 20 Apr 2012 07:48:25 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

h[t_] = Sin[t]; g[t_] = 2 UnitStep[t] - UnitStep[t - 1]; y[t_] = Integrate[h[t-s]g[s],{s,0,t}] results in a conditional expression requiring t>1, but I want to evaluate and plot t values from [0,1] as well as t>1. I tried HeavisideTheta as well as := in the definition of y to no avail. Thanks for any help... Your function g(s) is equal to 2 in the interval of your interest, i.e. from 0 to 1. Check: Plot[2 UnitStep[t] - UnitStep[t - 1], {t, -1, 2}] If the edges are not principally important to you, you may simply integrate and plot here y[t_] = Integrate[h[t-s]*2,{s,0,t}] Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L-5326 Contern, LUXEMBOURG Office phone : +352-2454-2566 Office fax: +352-2454-3566 mobile phone: +49 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu