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MathGroup Archive 2007

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Convolution Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72698] Convolution Integral
  • From: Mr Ajit Sen <senra99 at yahoo.co.uk>
  • Date: Tue, 16 Jan 2007 02:07:09 -0500 (EST)

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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