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| − | =[[HW6_ECE301_Spring2011_Prof_Boutin| | + | =[[HW6_ECE301_Spring2011_Prof_Boutin|HW6]] discussion, [[2011_Spring_ECE_301_Boutin|ECE301 Spring 2011, Prof. Boutin]]= |
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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? | 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 | |
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In problem 5b should that be +2jw in the numerator of <math> X(w) </math> instead of -2jw? It looks like a time shift of <math> t_0=2 </math> and then <math>e^{-at}u(t) = \frac{1}{a+i\omega}</math>. | In problem 5b should that be +2jw in the numerator of <math> X(w) </math> instead of -2jw? It looks like a time shift of <math> t_0=2 </math> and then <math>e^{-at}u(t) = \frac{1}{a+i\omega}</math>. | ||
| + | :No, the answer is correct. Yes, the signal considered is a time delay (of two time units) of the signal <math class="inline">e^{-at}u(t) </math>. But if you recall, the time shifting property is: | ||
| + | :<math>{\mathcal F} \left( x(t-t_0) \right) = e^{-j \omega t_0} {\mathcal X} (\omega) </math> | ||
| + | :so, the numerator of <math class="inline"> {\mathcal X}(\omega) </math> is <math class="inline">e^{-2 j \omega}</math>. 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 <math>\omega</math>. This would get marked off in a test. -pm | ||
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Revision as of 16:21, 5 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
