# Fourier Representation of Simple Half-Wave Rectifier

1. Nov 4, 2004

### cj

I, in fact, know the correct Fourier representation
for the following (it was given to me):

$$f(t)=0 \text { if } -\pi \leq \omega t \leq 0$$

and

$$f(t)=sin(\omega t) \text { if } 0 \leq \omega t \leq \pi$$

$$\hrule$$

I'm curious about the derivation that led to it -- specifically how the coefficients were derived.

I know, in general...

$$A_0=\frac{1}{2\pi} \int_{-\pi}^{\pi}f(x)dx$$

$$A_N=\frac{1}{\pi} \int_{-\pi}^{\pi}f(x)cos(nx)dx$$

$$B_N=\frac{1}{\pi} \int_{-\pi}^{\pi}f(x)sin(nx)dx$$

... but am stuck when it comes to setting-up the
integrals (substitution rules, how integrals might be broken-up into sub-integrals, intervals, etc.)