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Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

  1. Aug 18, 2012 #1
    1. The problem statement, all variables and given/known data

    I am using the time differentiation property to find the fourier transform of the following function:


    2. Relevant equations

    f(t)=2r(t)-2r(t-1)-2u(t-2)

    3. The attempt at a solution
    f'(t)=2u(t)-2u(t-1)-2δ(t-2)
    f''(t)=2δ(t)-2δ(t-1)-???????

    Can somebody explain what the derivative of the dirac delta function is?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 18, 2012 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    The easiest way to see what [itex]\frac{d}{dx}\delta(x)[/itex] is, is to multiply it by a simple test function like [itex]x[/itex] and Integrate over any interval enclosing the origin, using integration by parts.
     
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