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The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
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Fourier transform of $\cos(n\omega t)$
Let's take a look at the first half of your expansion; $cos(6\pi f_{0} t)$
The Fourier transform for this would be
\begin{equation}
X_{c}(j\Omega) = \pi \delta(\Omega - 6\pi f_{0}) + \pi \delta( …