Latest revision as of 14:19, 10 March 2011

HW6 discussion, ECE301 Spring 2011, Prof. Boutin

If they make a silly math mistake, like off by a negative, and carry it thought and all the steps are right should we take off?

This is something you will have to decide. Personally, I first look whether there was an easy "common sense" way to see that mistake at the end. For example, if the student is computing an energy and ends up with a negative quantity, this is an important mistake (because energies are always non-negative). But if the minus sign is truly just a tiny detail and the problem had a lot of non-trivial steps, all of which were done perfectly, then I won't take off any point. Not all graders do this, of course... -pm

In problem 5b should that be +2jw in the numerator of $ X(w) $ instead of -2jw? It looks like a time shift of $ t_0=2 $ and then $ e^{-at}u(t) = \frac{1}{a+i\omega} $.

No, the answer is correct. Yes, the signal considered is a time delay (of two time units) of the signal $ e^{-at}u(t) $. But if you recall, the time shifting property is:

$ {\mathcal F} \left( x(t-t_0) \right) = e^{-j \omega t_0} {\mathcal X} (\omega) $

so, the numerator of $ {\mathcal X}(\omega) $ is $ e^{-2 j \omega} $. A side note: the last equation you wrote is clearly false, because the left-hand-side is a function of t, and the right-hand-side is a function of $ \omega $. This would get marked off in a test. -pm

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