Re: Convolution Integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg72752] Re: [mg72698] Convolution Integral*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Wed, 17 Jan 2007 07:36:59 -0500 (EST)*Reply-to*: hanlonr at cox.net

convolve[f_,g_]:=Integrate[f[u]*g[t-u],{u,0,t}]; convolve[Sin,Exp[-#]&] (1/2)*(E^(-t) - Cos[t] + Sin[t]) Bob Hanlon ---- Mr Ajit Sen <senra99 at yahoo.co.uk> wrote: > Dear Mathgroup, > > Could anyone please help me with the following? > > I'd like to find the convolution of 2 arbitrary > functions, f(t) and g(t) in the Laplace transform > sense,i.e., > > convolve[f[t],g[t]]=Integrate[f[u]*g[t-u],{u,0,t}] > > Thus, I'd like convolve[Sin[t],Exp[-t]] to return > > (Exp[-t]-Cos[t]+Sin[t])/2 . > > My several attempts with function definitions such as > > convolve[f_,g_]:=Integrate[f[u]*g[t-u],{u,0,t}] > > > convolve[f[t_],g[t_]]:=Integrate[f[u]*g[t-u],{u,0,t}] > > convolve[f_,g_][t_]:=Integrate[f[u]*g[t-u],{u,0,t}] > > all failed (because of the dummy u ? ) > > Thanks in advance. > Sen.