Fourier transform of $\sin(2\pi fm t) \sin(2\pi fc t) $

Asked Mar 28 '16 at 21:33

Active Mar 28 '16 at 22:09

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How do I find the Fourier transform of $\sin(2\pi f_m t)\sin(2\pi f_c t) $?

My main confusion comes from $fm$ and $fc$. If I had the same frequency I could of used a trig identity and then Fourier transform it but with different frequencies I'm unsure what to do.

edited Mar 28 '16 at 22:09

asked Mar 28 '16 at 21:33

a wee little worker

What kind of numbers are $f_m$ and $f_c$? (I'm assuming you meant to put subscripts.) – Cameron Williams Mar 28 '16 at 21:34
Instead I think $f$ is a frequency and $m$ and $c$ are integer numbers. – Vincenzo Tibullo Mar 28 '16 at 21:36
3

You can use $\sin(a)\sin(b) = \frac{1}{2}(\cos(a-b) - \cos(a+b))$ – Mar 28 '16 at 21:39
$\mathscr F { cos(at) }=\frac{1}{2} (\delta (f-a)+\delta (f+a))$ – K.K.McDonald Mar 28 '16 at 22:11
Start with $ \sin(2\pi f_m t)\sin(2\pi f_c t) = \frac{1}{2}\left[\cos(2\pi(f_m-f_c)t)+\cos(2\pi(f_m+f_c)t)\right] $ – Disintegrating By Parts Mar 29 '16 at 03:27

Fourier transform of $\sin(2\pi fm t) \sin(2\pi fc t) $

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