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...
>

```

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