*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 | +---------------------------------+