Re: convolution involving UnitStep

*To*: mathgroup at smc.vnet.net*Subject*: [mg126145] Re: convolution involving UnitStep*From*: John Davis <texasautiger at gmail.com>*Date*: Fri, 20 Apr 2012 07:49:27 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201204190754.DAA04280@smc.vnet.net>

I agree this works, but am perplexed as to why my straightforward computation (unexpectedly) gives Mathematica trouble. Thanks for your help, John On Thu, Apr 19, 2012 at 8:15 AM, Bob Hanlon <hanlonr357 at gmail.com> wrote: > h[t_] = Sin[t]; > > g[t_] = Piecewise[{{0, t < 0}, {2, 0 <= t < 1}}, 1]; > > y[t_] = Assuming[{Element[{s, t}, Reals]}, > Integrate[h[t - s] g[s], {s, 0, t}] // Simplify] > > Piecewise[{{1 + Cos[1 - t] - 2*Cos[t], t > 1}, > {2 - 2*Cos[t], Inequality[0, Less, t, LessEqual, > 1]}}, 0] > > > Bob Hanlon > > > On Thu, Apr 19, 2012 at 3:54 AM, J Davis <texasautiger 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... > > >

**References**:**convolution involving UnitStep***From:*J Davis <texasautiger@gmail.com>