Math Help - Fourier Series involving modulus

1. Fourier Series involving modulus

Hi,

I have this question:

Calculate the fourier series for g(t) = 2 - 2|cos(t/2)|

I've sketched the graph so I know that that the function is even, meaning that bn=0, and it has period of 2*pi (from -pi to pi). However i just can't seem to work out how to deal with the modulus. I think i have to split the integrals into two parts, is this right?

Please help,
Katy

2. Originally Posted by harkapobi
Hi,

I have this question:

Calculate the fourier series for g(t) = 2 - 2|cos(t/2)|

I've sketched the graph so I know that that the function is even, meaning that bn=0, and it has period of 2*pi (from -pi to pi). However i just can't seem to work out how to deal with the modulus. I think i have to split the integrals into two parts, is this right?

Please help,
Katy
Yes, of course, just like you always do with absolute values, do x< 0 and x> 0 separately.

3. Originally Posted by HallsofIvy
Yes, of course, just like you always do with absolute values, do x< 0 and x> 0 separately.
I thought so. I may be being really dumb here, but I really can't figure out how this affects the integrals. Would it be:

2 - 2 cos(t/2) for t>0
2 + 2cos(t/2) for t<0 ?