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Re: Convolution Integral


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.


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