Fourier Series for real and odd signals

[awelex]

Hi,

I have a general question regarding the computation of Fourier Series coefficients for real and odd inputs. In this case, the following should be true:

∫x(t)*e^(-j*k*w*t)dt = ∫x(t)*sin(k*w*t)dt

However, every time I compute my coefficients this way, I get the inverse sign of what it is supposed to be -- my coefficients are flipped on the x-axis. Since this happens every time, I don't think it's a computational mistake, but rather a conceptual problem. What am I doing wrong?

Thanks.

 

[awelex]

A second after posting this, I think I figured it out:

Since e^(-j*w*t) = cos(w*t) - j * sin(w*t), I'm missing a minus sign in my integral. Correct?

 

[AlephZero]

It's either that, else or your integral should be ∫x(t)*sin(k*-w*t)dt