Homework Six

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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.