# Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

1. Aug 18, 2012

### p75213

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. Aug 18, 2012

### gabbagabbahey

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