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
