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,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44
e-mail: alexei.boulbitch at iee.lu