Re: Convolution Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg72749] Re: Convolution Integral
• From: dh <dh at metrohm.ch>
• Date: Wed, 17 Jan 2007 07:24:55 -0500 (EST)
• Organization: hispeed.ch
• References: <eoht0r\$pti\$1@smc.vnet.net>

```Hi,
if you have problems with dummy variables, it makes sense to  work with
pure functions, e.g. Function[x,expression(x)] or expression(#) (note
the default variable #)&. E.g.
conv[f1_, f2_] := Module[{u}, Evaluate[Integrate[f1[u] f2[# -
u],{u,0,#}] ] &]
the "Evaluate" is necessary because (..)& does not evaluate its
arguments. Now, try e.g. f=conv[Cos, Sin[# + .1] &], this gives another
pure function that can be evaluated by e.g.: f[0.3]
Daniel

Mr Ajit Sen wrote:
> Dear Mathgroup,
>
>
>  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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>

```

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