Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem on integrating dirac delta function

  1. May 6, 2012 #1
    Hi there,
    I am trying to integrate this: http://imm.io/oqKi
    I should get the second line from the integral, but I can't show it.
    This should somehow relate to the Heaviside step function, or I am completely wrong.
    Any ideas?

    Sorry about the url, I fixed it.
     
    Last edited by a moderator: May 6, 2012
  2. jcsd
  3. May 6, 2012 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    What is "imm.io/oqKi "??????
     
  4. May 6, 2012 #3

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Anyhow, whatever "imm.io/oqKi " is:

    The Dirac delta "function" isn't a function in the usual sense, so can't integrate it in the usual sense, either.
     
  5. May 6, 2012 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The "Dirac delta funtion" is not really a function, as arildno says. It is a "generalized function" or "distribution"- a linear operator on functions.

    By definition
    [tex]\int_a^b f(x)\delta(x)dx= f(0)[/tex]
    if a< 0< b, 0 otherwise.

    That means that
    [tex]\int_a^b \delta(g(x))f(x) dx= f(c)[/tex]
    if g(c)= 0 for some c between a and b.
     
  6. May 6, 2012 #5
    This makes sense for why they put [tex](x-x_0)\cos(\theta)+(y-y_0)\sin(\theta)=0[/tex] after the second line.

    Actually I am in the middle of proving the simple backprojection of the Radon transform of a dot can be viewed as a two dimensional convolution of [tex]\frac{1}{\sqrt{x^2+y^2}}[/tex] and the original function. I used the Dirac Delta to formulate the dot, so this is just for the convenience of prove.

    The Dirac Delta also has this property:[tex]\int\delta(\alpha x)dx = \frac{1}{|\alpha|}[/tex], I think this might help.
     
    Last edited: May 6, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem on integrating dirac delta function
  1. Dirac Delta function (Replies: 44)

  2. Dirac Delta function (Replies: 1)

Loading...