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Dirac Delta Cosx

  1. Mar 10, 2008 #1
    1. The problem statement, all variables and given/known data
    The function [tex]\delta(cosx)[/tex] can be written as a sum of Dirac delta functions:
    [tex]\delta(cosx)=\sum_{n} a_{n}\delta(x-x_{n})[/tex]
    Find the range for n and the values for [tex]a_{n}[/tex] and [tex]x_{n}[/tex]


    3. The attempt at a solution
    Well, taking the integral of [tex]\delta(cosx)[/tex], we only get spikes when x is an even multiple of [tex]\frac{\pi}{2}[/tex]. So shouldn't n run to infinity? Thats all i have so far, any help would be appreciated. thanks.

    -Adrian
     
  2. jcsd
  3. Mar 10, 2008 #2

    Dick

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    Homework Helper

    You get 'spikes' where cos(x)=0. I wouldn't describe those as 'even multiples of pi/2'. In general if x_i are the roots of f(x)=0, then delta(f(x)) is the sum of delta(x_i)/|f'(x_i)|.
     
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