FT of Unit step function

Created
Created
2023 Sep 27 2:36
Creator
Creator
Seonglae Cho
Editor
Edited
Edited
2023 Oct 10 16:21

Very Complex

Except t=0t=0, u(t)+u(t)=1u(t) + u(-t) = 1 and using
FT of a Constant
2πδ(w)=U(jw)+U(jw)2\pi\delta(w) = U(jw) + U(-jw)
Let U(jw)=kδ(w)+V(jw)U(jw)= k\delta(w) + V(jw) then
  • odd part of
2πδ(w)=2kδ(w)+V(jw)+V(jw)2\pi\delta(w) = 2k\delta(w) + V(jw) + V(-jw)
k=πk=\pi and V(jw)V(jw) is odd function
by
CTFT Differentiation
and δ(t)=tdtu(t)\delta(t) = \frac{t}{dt}u(t)
 
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notion image
 
 
 
 
 

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