Understanding Fourier Coefficients for Step Functions: Homework Help

[Nusc]

Homework Statement

f(t) = 1 0<=t<T/2
-1 T/2 <=t<=T

ie. step function.frequency w_0 = 2pi/T

Homework Equations

The Attempt at a Solution

What's the definition for the Fourier coefficients a_n and b_n again? Not the one in wikipedia.

 

[Dr.D]

Show us the work you have done on this. There are defining integrals for these coefficients, so set them up and try evaluating them.

 

[Nusc]

$$<br /> a_n = \frac{1}{\pi} \int_0^{T/2} 1*cos(nt) dt +\frac{1}{\pi} \int_{T/2}^{T} (-1)*cos(nt) dt$$

$$<br /> b_n = \frac{1}{\pi} \int_0^{T/2} 1*sin(nt) dt +\frac{1}{\pi} \int_{T/2}^{T} (-1)*sin(nt) dt$$

I think the normalization factor is incorrect, which is why i asked for the definition, I think it was 2/L where L is the length of the interval - i can't remember.

 

[Dr.D]

If you can't remember, do you have a book?

 

[Nusc]

No, that's why I asked.