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MathGroup Archive 2007

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Re: Convolution Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72745] Re: Convolution Integral
  • From: Bill Rowe <readnewsciv at sbcglobal.net>
  • Date: Wed, 17 Jan 2007 07:08:51 -0500 (EST)

On 1/16/07 at 2:07 AM, senra99 at yahoo.co.uk (Mr Ajit Sen) wrote:

>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}]

This definition works fine *if* you supply pure functions as 
arguments, i.e.,

In[3]:=
convolve[f_,g_]:=Integrate[f[u]g[t-u],{u,0,t}]

In[4]:=
convolve[Sin[#]&,1/Exp[#]&]

Out[4]=
(1/2)*(-Cos[t] + E^(-t) + Sin[t])
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