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MathGroup Archive 1998

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Re: Convolution


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10938] Re: Convolution
  • From: calvitti@lychee.ces.cwru.edu
  • Date: Sat, 14 Feb 1998 00:53:13 -0500
  • In-Reply-To: Larry Gottlob's message of 12 Feb 1998 06:37:02 -0500
  • Organization: Case Western Reserve University
  • References: <6bumsu$l93@smc.vnet.net>

>>>>> "L" == Larry Gottlob <lrg@geri.duke.edu> writes:

    L> I'm not experienced at Mathematica.  I define two functions:
    L> Func1[x_] := tau*Exp(-x)      Func2[x_] := mu*x^2
    L> for instance, where tau and mu are constants.

    L> How do I define a function of x that is a convolution of Func1
    L> and Func2, and plot that?
 
you're probably going to have trouble taking the convolution of those
two functions since their integrals diverge. convolution of f and g is
defined as:

    convolution[f_,g_,x_] := Integrate[f(y)*g(x-y),y]

you can plot convolution[Func1,Func2,x] like any other function.
alternatively, 

1) convolution is also the inverse fourier transform of the product of
the fourier transforms of the f and g

2) use the discretized approximation Sum[f[x]*g[x],{x,-M,M}] where M is
a large number. if you use this method, it's probably much faster to
build up a list (with Table) to represent the convolution over a
specific interval at a specific gridsize...then use ListPlot to plot
it:

 discreteConvolution[f_,g_,x_,x0_,x1_,dx_,M_] :=
 Table[Sum[f[x]*g[y-x],{x,-M,M}],{y,x0,x1,dx}];

 +---------------------------------+
 |          Alan Calvitti          |
 | Systems and Control Engineering |
 |    Autonomous Robotics Group    |
 | Case Western Reserve University |
 +---------------------------------+




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