Re: convolution involving UnitStep
- To: mathgroup at smc.vnet.net
- Subject: [mg126126] Re: convolution involving UnitStep
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Fri, 20 Apr 2012 07:42:53 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201204190754.DAA04280@smc.vnet.net>
Boole also works h[t_] = Sin[t]; g1[t_] = Piecewise[{{0, t < 0}, {2, 0 <= t < 1}}, 1]; g2[t_] = 2 Boole[0 <= t < 1] + Boole[1 <= t]; y1[t_] = Assuming[{Element[t, Reals]}, Integrate[h[t - s] g1[s], {s, 0, t}] // Simplify]; y2[t_] = Assuming[{Element[t, Reals]}, Integrate[h[t - s] g2[s], {s, 0, t}] // Simplify]; y1[t] === y2[t] True Bob Hanlon On Thu, Apr 19, 2012 at 9:31 AM, John Davis <texasautiger at gmail.com> wrote: > I agree this works, but am perplexed as to why my straightforward > computation (unexpectedly) gives Mathematica trouble. > > Thanks for your help, > John > > > > On Thu, Apr 19, 2012 at 8:15 AM, Bob Hanlon <hanlonr357 at gmail.com> wrote: >> >> 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