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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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Reconstructing an undersampled signal by cutting off at the signal's maximum frequency
Assume a (continuous) band-limited signal $f$, that is, a signal for which $F(s) = 0$ for all $\lvert s \rvert > p / 2$.
If the signal is sampled with frequency $p$,
we can reconstruct it by cutting o …