Re: convolution involving UnitStep
- To: mathgroup at smc.vnet.net
- Subject: [mg126144] Re: convolution involving UnitStep
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Fri, 20 Apr 2012 07:49:07 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201204190754.DAA04280@smc.vnet.net>
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...
>
- References:
- convolution involving UnitStep
- From: J Davis <texasautiger@gmail.com>
- convolution involving UnitStep