Re: convolution involving UnitStep

*To*: mathgroup at smc.vnet.net*Subject*: [mg126123] Re: convolution involving UnitStep*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>*Date*: Fri, 20 Apr 2012 07:41:51 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jmogf6$46k$1@smc.vnet.net>

On 19 Apr., 09:56, J Davis <texasauti... at gmail.com> wrote: > 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... > > I can't confirm any trouble in 5.2: In[1]:= h[t_] = Sin[t]; g[t_] = 2*UnitStep[t] - UnitStep[t - 1]; y[t_] = Integrate[h[t - s]*g[s], {s, 0, t}] Out[3]= (-1 + Cos[1 - t])*UnitStep[-1 + t] - 2*(-1 + Cos[t])*UnitStep[t] Best regards Wolfgang