# Fourier series neither odd nor even

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1. May 2, 2016

### Nemo's

1. The problem statement, all variables and given/known data
I'm trying to calculate the Fourier Series for a periodic signal defined as:

y = x 0<x<2Π
y = 0 2Π≤x<3Π

2. Relevant equations
Fn = 1/T ∫T f(t)cos(kwοt + θk)

cn/2 + ∑k=1k=∞(cn)cos(kwοt+θk)
cn= 2|Fn|
θk=∠Fn

3. The attempt at a solution
I got Cn = -(√3/ +9/4Π)
θk = -kwοt

The problem with this value for θk is that k disappears from the summation. I need this formula to be able to regenerate the original signal from it's fourier series coefficients using matlab. I must be doing something wrong. I would really appreciate it if someone told me what to do.

Last edited: May 2, 2016
2. May 2, 2016

### Simon Bridge

Try using a more general fourier series with both sine and cosine in it.
Looking at your function - is it better served by a sum of cosines or a sum of sines?

3. May 3, 2016

### Nemo's

My function is neither odd nor even so it has to be represented using both sines and cosines right?
I thought the formula I'm using above works fine for all real functions. In fact the first part of the question asked me to prove this.
I'll try using the general form anyway and post the results.

4. May 5, 2016

### rude man

You're quite right, in that form it can represent any real periodic function.
But you haven't defined your function too well. Does it repeat below x=0 and above x=3pi?