Question

Taking limit of series

Answer 1

\[\lim_{N \rightarrow \infty} \frac{ 1 }{ 2N + 1 } \sum_{n=-N}^{N}\left| \sin(n*\frac{ \Pi }{ 4 } \right|\]

Answer 2

I'm confused how you would use the capital N's

Answer 3

mathematica says the answer should be 1/4 + sqrt(2), but i'm not sure how to get to that answer

Answer 4

I would start by writing sin as imaginary part of \(\large e^{in\pi / 4}\)

Answer 5

then see if it gives a geometric series and find the partial sum

Answer 6

then take the limit

Answer 7

just thoughts ^^ not sure if its that easy

Answer 8

how do you do that with -N to N though?

Answer 9

yah think there must be a trick to this that I am missing because this is the first week of class and this seems like a ridiculous equation to use so early in the class

Answer 10

is this q from complex analysis ?

Answer 11

naw, it's from an electrical engineering class, signals and systems

Answer 12

I was just reading some more and it looks like you are right to switch it to the imaginary form. However, the signal coming in is periodic so you can use some related equations for 1 iteration of the signal and then repeat

Answer 13

looks like i have some more reading to do :)

thank you very much for the help though

Answer 14

good luck !