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# Fourier Series watch

1. Hi,

I'm having trouble with a fourier series question and was wondering if anyone could help.

basically we have to expand the periodic function f(x) in a sine-cosine fourier series where:

between and
between and
between and

and has a period of

Our lecturer gives the answer as:

I managed to sketch the function and get the first half right (the 1/4 term and the cos terms), but I can't figure out how to get those sin terms.

I used between pi and minus pi. Did 3 seperate integrals, 2 of which are 0 so got:

substituting in n = 1,2,3,4,5,6
all the odd terms = 0

so end up with my answer as:

Does anyone know where I've gone wrong, or how to get from my answer to the one he's given?

Any help would be much appreciated
2. I have no idea but I thought I'd bump your post in case anyone does since you posted it in the middle of the night
3. (Original post by Slothzilla)
I have no idea but I thought I'd bump your post in case anyone does since you posted it in the middle of the night
Haha thanks
4. Are you a maths or engineering student?

You have not gone wrong.

As you say all the odd terms are zero. This is a rectangular pulse time shifted and the series is convergent.

Your lecturer seems to have a copying error or it could be he's trying to see if students are awake!

Either way the 2sin2x/2 is incorrect (shouldn't be there) as are the signs, which should alternate +/- in that part of the expansion. The cosine terms should all be odd (alternating signs) and the sine terms are all even.

Here's a great site for some real insights into signal processing:

http://www.fourier-series.com/f-transform/index.html
5. (Original post by uberteknik)
You have not gone wrong.

As you say all the odd terms are zero. This is a rectangular pulse time shifted and the series is convergent.

Your lecturer seems to have a copying error or it could be he's trying to see if students are awake!

Either way the 2sin2x/2 is incorrect as are the sign terms in that part of the expansion.

Here's a great site for some real insights into signal processing.
I have, figured it out now though! when I subsituted the limits into my integral I forgot that cos(0) = 1 (I'm so used to just taking the upper limit as the integral when the lower limit is 0, I blame tiredness...). so I end up with instead of what I put in the OP. The 1/n term ends up making my result the same as the answer he gave

Thanks for the site, seems like it could be pretty helpful!
6. Ha ha. Well done!

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