Perform the following tasks:
Nick Christman
(a) Show . HINT:
(b) If can you find in terms of ?
(c) Do another property on the Wiki and get it reviewed (i.e. review a second property) -- Fourier Transform Properties
(i) Find
-- Using the above definition of complex modulation and the definition from class of a time delay (a.k.a "the slacker function"), I will attempt to show a hybrid of the two...
By definition we know that:
Rearranging terms we get:
Now lets make the substitution .
This leads us to:
After some simplification and rearranging terms, we get:
Rearranging the terms yet again, we get:
We know that the exponential in terms of is simply a constant and because of the Fourier Property of complex modualtion, we finally get:
(ii)
I reviewed Max's second Fourier Transform property:
As near as I can tell, it all looks legitimate. I made one comment about adding an additional step to make the proof/identity more complete, but that was all that I could find.