- #1
Moomax
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Homework Statement
Evaluate INT(|X(t)|^2) dt using parsevals theorem
where x(t) = (sin(t)cos(10t))/(pi*t)
Homework Equations
parsevals theorem: int(|f(t)|^2 dt = (1/2*pi)INT(|F(W)|^2 dw
The Attempt at a Solution
So I've tried several attempts at this problem and this is my latest:
first I use the fact that sin(x)*cos(y) = (sin(x+y)+sin(x-y)) /2
to get sin(t)cos(10t)/pi*t = (sin(t+10t) + sin(t - 10t))/(2*pi*t)
then I split it up into : sin(11t)/2t*pi + sin(-9t)/2t*pi
then what I was going to do was take the Fourier transform of each function here however, I can't figure out how in the world to take the Fourier transform of sin(t)/t
anyone have any ideas? thanks!