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Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

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p75213
#1
Aug18-12, 05:58 AM
P: 89
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
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gabbagabbahey
#2
Aug18-12, 06:16 AM
HW Helper
gabbagabbahey's Avatar
P: 5,003
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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