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.