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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



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