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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...
> >
>




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