Unit step function Definition and 55 Threads

how can I calculate the Fourier transform for unit step function: v(t)=1 where 0=<t<+infinity v(t)=0 otherwise I applied the general definition relation for FT: v(w)=integral(v(t)*e^-jwt) ; - infinity<t<+infinity but i had v(w)=infinity due to the term infinity-displaced e^(+jwt)...

hello maths experts is the following true? http://img9.imageshack.us/img9/4596/int15oe.jpg graphically, this is how i view it http://img9.imageshack.us/img9/179/int28ut.jpg

I have some trouble wrapping my head around singularity One of assignment question is to show that the unit function is not defined at 0. To do that, I need to show \lim_{\Delta\to0}[u_{\Delta}(t)\delta(t)]=0 \lim_{\Delta\to0}[u_{\Delta}(t)\delta_{\Delta}(t)]=\frac{1}{2}\delta(t)...

Hey I was wondering if someone would check my work on this problem: Note: {\cal L} = Laplace {\cal U} = Unit Step Function {\cal L} \{ \cos(2t) \,\,\, {\cal U} (t - \pi)\} =e^{-\pi s} {\cal L} \{ \cos(2(t + \pi)) \} =e^{-\pi s} {\cal L} \{ \cos(2t + 2\pi) \} =e^{-\pi s}...

[SOLVED] Derivative of unit step function How does one do this, for example x= e^(-3t)u(t-4); how do you get x' ??