I, in fact, know the correct Fourier representation(adsbygoogle = window.adsbygoogle || []).push({});

for the following (it was given to me):

[tex]f(t)=0 \text { if } -\pi \leq \omega t \leq 0[/tex]

and

[tex]f(t)=sin(\omega t) \text { if } 0 \leq \omega t \leq \pi [/tex]

[tex] \hrule [/tex]

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

I know, in general...

[tex]A_0=\frac{1}{2\pi} \int_{-\pi}^{\pi}f(x)dx[/tex]

[tex]A_N=\frac{1}{\pi} \int_{-\pi}^{\pi}f(x)cos(nx)dx[/tex]

[tex]B_N=\frac{1}{\pi} \int_{-\pi}^{\pi}f(x)sin(nx)dx[/tex]

... but am stuck when it comes to setting-up the

integrals (substitution rules, how integrals might be broken-up into sub-integrals, intervals, etc.)

Comments?

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# Fourier Representation of Simple Half-Wave Rectifier

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