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Topic: Dirac in Convolution
Replies: 1   Last Post: Mar 13, 2013 9:19 AM

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Christopher Creutzig

Posts: 323
Registered: 2/24/09
Re: Dirac in Convolution
Posted: Mar 13, 2013 9:19 AM
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On 10.03.13 20:58, omid najafi wrote:
> in this program
> -----------------------------------------------------
> clear;clc
> dx=0.01;
> x=-2:dx:2;
> f1=heaviside(x+1)-heaviside(x-1);
> f2=dirac(x-1);
> f3=dx*conv2(f1,f2);
> xc=-4:dx:4;
> subplot(3,1,1);plot(x,f1)
> subplot(3,1,2);plot(x,f2)
> subplot(3,1,3);plot(xc,f3)
> -----------------------------------------------------
> we know
> int(dirac(x-a)*f(x),-inf, inf) = convolution(dirac(x-a),f(x)) = f(x-a)

conv2 doesn't know that. It assumes you mean a discrete convolution
(where using dirac doesn't really make sense, unless you want a
distribution back). By the time f2 is defined, your dirac has already
gone numeric (i.e., it is 0 or Inf), and any such connection is lost.
Write the integral form instead, with a symbolic x.


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