Re: convolution involving UnitStep

• To: mathgroup at smc.vnet.net
• Subject: [mg126142] Re: convolution involving UnitStep
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Fri, 20 Apr 2012 07:48:25 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```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...

Your function g(s) is equal to 2 in the interval of your interest, i.e. from 0 to 1.
Check:

Plot[2 UnitStep[t] - UnitStep[t - 1], {t, -1, 2}]

If the edges are not principally important to you, you may simply integrate         and plot here

y[t_] = Integrate[h[t-s]*2,{s,0,t}]

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
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Office phone :  +352-2454-2566
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e-mail: alexei.boulbitch at iee.lu

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