Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

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Homework Statement



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


Homework Equations



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

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?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
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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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