wtf is the the exponential form fourier series of sin^4(x) I

>>7923226
show your work, will tell you where you made a mistake.

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for all n the thing is zero

>>7923233
my book shows something with l'hopitals rule when the top and bottom are zero so it might have something to do with that but idk

help me guys I thought you motherfuckers were good at math

>>7923378
Everything looks airtight to me. Sorry brother have a bump

>>7923249
Woah.

My first reaction is to just evaluate the frequency domain convolutions. Since each of the sin terms will just be a Delta function in frequency domain, the convolution will just be a bunch of phase shifted Delta's. Taking the inverse transform would then yield a sum of sines.

>>7923430
so it is zero?

>>7923440
well we cant use your advanced shit because we are just learning the fourier series in my signal processing class

>>7923452
I learned laplace transforms before fourier series expansions. Have you taken differential equations before? I didn't learn about the complex form until after that class anyway, so you should be familiar with it.

>>7923452
Yeah, and they should have taught you the multiplication and convolution properties for Fourier series. The properties are there to save your ass from doing pages of work.

>>7923455
yeah I've taken diff eq but we didnt cover laplace we only went up to the trig fourier

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this is a table in my book

this is all i have to solve fourier with

>>7923226
Do the Fourier transform of sin(x)=e^ix-e^-ix/2i
Perform convolution to get sin^2(x)= 1/2-(e^i2x+e^-i2x)/4
Perform convolution to get sin^4(x)= 3/8-(e^i2x+e^-i2x)/4+(e^i4x+e^-i4x)/16

>>7923480
i already did that

>>7923484
so what the fuck? you have the answer right there

post your work fgt

>>7923490
nigga thats not the answer
do you know what a fourier series is?

I have to solve the intergral of that answer times e^(-j2nt) from 0 to pi to get the fourier coefficient

>>7923493
Apparently you have no clue what a Fourier series is. Any sum of complex exponentials IS a Fourier series...

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>>7923493
do you see this shit?

f(t) is sin^4(x) and i have to solve for the coefficient for the exponential form

>>7923499
lul replied to myself

but see >>7923504

:(

>>7923506
Huh, so maybe what you want then are the coefficients of the exponentials?

>>7923527
i just need to solve the integral and I already showed my work but i get zero and idk if that is right

why you guys all misspell i?

>j. not even once.

>>7923535
nigga this electrical engineering we use j because i means current

>>7923531
There is nothing to integrate here.

You need to review what exactly a Fourier series is, and how to determine the Fourier coefficients of sine and cosine by inspection. Your making this way harder than it actually is, because you don't really know what you're looking for.

This is like a two to four line solution with zero calculus required.

>>7923563
so what you're telling me that the exponential form fourier series of sin(x) IS (e^jx - e^-jx)/2j

>>7923226
Literally expand sin(x)^4 to get (3/8) - (1/2)cos(2x) + (1/8)cos(4x). That is the fourier series. Fuck with the form to get it where you want. You don't need to integrate shit.

>>7923598
Exactly. The coefficients then are nothing more than the coefficients of the exponentials (j/2 and -j/2).

So you have two approaches to this problem that don't involve integrating anything. Either take that expression to the fourth power, then look at what the coefficients are, or use the multiplication property twice.

>>7923615
>>7923617
holy fucking cow tits
it all makes sense now

thank you anons, doing god's work

>>7923623
Just curious, what book are you using, and what class is this for?

If this is an actual Signals and Systems class (and not just a circuit analysis course), then that table of properties is sorely lacking.

Do you go go UCLA senpai and have Cabric as your teacher

>>7923627
that book is analog signals and systems made by erhan kudeki, a professor at UIUC

>>7923631
sorry anon i goes to UIUC

>>7923637
> UIUC

My prof for Feedback Control Systems is from UIUC. Great school for EE from what I understand. That book seems shit though.