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| − | In question 2e | + | In question 2e |
<math> x(t)= \sum_{k=-\infty}^\infty \frac{1}{1+(x-7k)^2} \ </math> | <math> x(t)= \sum_{k=-\infty}^\infty \frac{1}{1+(x-7k)^2} \ </math> | ||
| − | should it be like this? | + | should it be like this? |
| − | <math> x(t)= \sum_{k=-\infty}^\infty \frac{1}{1+(t-7k)^2} \ </math> | + | <math> x(t)= \sum_{k=-\infty}^\infty \frac{1}{1+(t-7k)^2} \ </math> |
:<span style="color:red"> yes, it should be. The correction has been made. -pm</span> | :<span style="color:red"> yes, it should be. The correction has been made. -pm</span> | ||
| − | and I was trying to find out what the peak value is for this question but turns out to be very hard to calculate the sum | + | and I was trying to find out what the peak value is for this question but turns out to be very hard to calculate the sum |
| − | <math> \sum_{t=-\infty}^\infty \frac{1}{1+t^2} \ </math> and wolfram said answer is '''π * coth(π)'''. is there any easier way to do that? | + | <math> \sum_{t=-\infty}^\infty \frac{1}{1+t^2} \ </math> and wolfram said answer is '''π * coth(π)'''. is there any easier way to do that? Yimin. Jan 20 |
:<span style="color:green"> You do not have to evaluate the sum. In particular, you do not need the peak value of that functions. Try to guess the period directly by looking at the sum. If you have no idea how to do this, read this [[Hw1periodicECE301f08profcomments| page]] first. -pm </span> | :<span style="color:green"> You do not have to evaluate the sum. In particular, you do not need the peak value of that functions. Try to guess the period directly by looking at the sum. If you have no idea how to do this, read this [[Hw1periodicECE301f08profcomments| page]] first. -pm </span> | ||
| − | Yeah I'm just trying to figure out the infinite sum just for fun. | + | Yeah I'm just trying to figure out the infinite sum just for fun. Thanks. |
| − | :<span style="color:green">Oh excellent! I think this deserves [[ | + | |
| − | And for question 4, are we still using the tempo? so my guess is use step functions to cut out the rhythm we want? <span style="color:green"> (Yes, that's the idea. -pm)</span> | + | :<span style="color:green">Oh excellent! I think this deserves [[How to evaluate this sum ECE301S11|a page on its own]]. Let's try to involve the math folks for help.-pm</span> |
| − | Then put the whole line in one equation? that will become pretty messy I guess. Yimin | + | |
| − | : <span style="color:green"> Not too bad, if you think about it carefully. Each note can be written in a somewhat simple form. Then you just add all the notes together. -pm </span> | + | And for question 4, are we still using the tempo? so my guess is use step functions to cut out the rhythm we want? <span style="color:green"> (Yes, that's the idea. -pm)</span> Then put the whole line in one equation? that will become pretty messy I guess. Yimin |
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| + | :<span style="color:green"> Not too bad, if you think about it carefully. Each note can be written in a somewhat simple form. Then you just add all the notes together. -pm | ||
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| + | </span> | ||
| + | <span style="color:green" />For question 4 we only need the first second on the song? Right, we don't have to compress the entire song into second. | ||
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Revision as of 18:21, 24 January 2011
In question 2e
$ x(t)= \sum_{k=-\infty}^\infty \frac{1}{1+(x-7k)^2} \ $
should it be like this?
$ x(t)= \sum_{k=-\infty}^\infty \frac{1}{1+(t-7k)^2} \ $
- yes, it should be. The correction has been made. -pm
and I was trying to find out what the peak value is for this question but turns out to be very hard to calculate the sum
$ \sum_{t=-\infty}^\infty \frac{1}{1+t^2} \ $ and wolfram said answer is π * coth(π). is there any easier way to do that? Yimin. Jan 20
- You do not have to evaluate the sum. In particular, you do not need the peak value of that functions. Try to guess the period directly by looking at the sum. If you have no idea how to do this, read this page first. -pm
Yeah I'm just trying to figure out the infinite sum just for fun. Thanks.
- Oh excellent! I think this deserves a page on its own. Let's try to involve the math folks for help.-pm
And for question 4, are we still using the tempo? so my guess is use step functions to cut out the rhythm we want? (Yes, that's the idea. -pm) Then put the whole line in one equation? that will become pretty messy I guess. Yimin
- Not too bad, if you think about it carefully. Each note can be written in a somewhat simple form. Then you just add all the notes together. -pm
<span style="color:green" />For question 4 we only need the first second on the song? Right, we don't have to compress the entire song into second.
