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Homework Statement
Determine the Fourier series for the full-wave rectifier defined as
f(t) = sinωt for 0 < ωt < pi
-sinωt for -pi < ωt < 0
Homework Equations
The Attempt at a Solution
This looks like an even function, so bm = 0
Ao = 1/pi∫sinωt from 0 to pi
= 1/pi(-cos(ωt))/ω) from 0 to pi
= 2/piω
An = 2/pi∫sin(ωt)cos(nt) from 0 to pi (because the function is even)
=2/pi∫(0.5(sin(ωt-nt)+0.5(sin(ωt+nt)) from 0 to pi
=-1/pi(cos(ωt-nt)/(ω-n) + cos(nt+ωt)/(n+ω)) from 0 to pi
= -(cos(pi(ω-n))-1)/(n+ω) -(cos(pi(ω+n))-1)/(pi(n+ω))
I'm stuck at this part. I don't know how to simplify those or what that equals to and I've been looking around for a very long time trying to figure it out...any help?
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