Re: convolution involving UnitStep

*To*: mathgroup at smc.vnet.net*Subject*: [mg126134] Re: convolution involving UnitStep*From*: danl at wolfram.com*Date*: Fri, 20 Apr 2012 07:45:39 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jmogf6$46k$1@smc.vnet.net>

On Thursday, April 19, 2012 2:56:22 AM UTC-5, J Davis 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... A bit awkward, but could do: y[t_] = Piecewise[{{Integrate[h[t - s] g[s], {s, 0, t}, Assumptions -> 0 < t < 1], 0 < t <= 1}, {Integrate[h[t - s] g[s], {s, 0, t}, Assumptions -> t > 1], t > 1}}] Daniel Lichtblau Wolfram Research