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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



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