- #1
robgb
- 17
- 0
The Fourier Series!
Hi guys, I'm having a bit a trouble helping my daughter with this question on the Fourier series approximation:
The Fourier series for a real, odd function, f(t) can be written as:
f(t) = [SUM to infinity, n=1, of]: b[subscipt n] sin(nwt)
where f(t=T)=f(t) and w=(2[pie])/T
Prove that b[subscipt n] = 2/T [integral between T/2 & -T/2 of]: f(t)sin(nwt)dt
Sorry about not knowing how to do all the symbols etc, but if you write it out I'm pretty sure it makes sence.
Anyway, if anyone could give me a hand with how to go about proving this, it would be greatly appreciated.
Many thanks, Robert.
Hi guys, I'm having a bit a trouble helping my daughter with this question on the Fourier series approximation:
The Fourier series for a real, odd function, f(t) can be written as:
f(t) = [SUM to infinity, n=1, of]: b[subscipt n] sin(nwt)
where f(t=T)=f(t) and w=(2[pie])/T
Prove that b[subscipt n] = 2/T [integral between T/2 & -T/2 of]: f(t)sin(nwt)dt
Sorry about not knowing how to do all the symbols etc, but if you write it out I'm pretty sure it makes sence.
Anyway, if anyone could give me a hand with how to go about proving this, it would be greatly appreciated.
Many thanks, Robert.