Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

  • Thread starter p75213
  • Start date
  • #1
p75213
96
0

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
5,002
7
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.
 

Suggested for: Derivative of Dirac Delta - Fourier Transform - Time Differentitation Property

Replies
22
Views
818
  • Last Post
Replies
2
Views
953
  • Last Post
Replies
3
Views
422
  • Last Post
Replies
3
Views
878
Replies
1
Views
928
Replies
3
Views
976
Replies
3
Views
466
  • Last Post
Replies
14
Views
1K
  • Last Post
Replies
1
Views
347
Replies
2
Views
965
Top