F(w) is the Fourier transform of f(t). Write down the equation for F(w) in terms of f(t).
A rectangular pulse has height H and total length t0 in time. Show that as a function of w, the amplitude density is propertional to sinc(wt0/2).
F(w) = integral from -infinity to +infinity of: f(t)exp(-iwt)dw
The Attempt at a Solution
integral from -t0/2 to +t0/2 of: h*exp(-iwt)dw
I have access to the solution to this problem, which says that it should be:
integral from -t0/2 to +t0/2 of: h*exp(-iwt)dt,
but I don't understand why I'm integrating wrt t now, when the definition says w.
Could somebody please explain this?
Thanks in advance.