# Periodic graph in frequency domain

Why is that the frequency domain has the same shape all through out? Look at figure b

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The short answer is that when computing the spectrum of a signal, we are applying the Fourier transform (or something fancier, but let's stay with that). What happens is that every signal that is discrete in time, will be periodic in frequency, and vice versa.

For the same reason, if you have a perfect sinewave, it will be a single spike in the spectrum.

A consequence of this phenomenon is aliasing: these copies of the spectrum are separated by the sampling frequency (the frequency at which the signal is measured); if it's too low (less than 2*fmax) these copies will merge and you'll lose detail about the original signal. This is the Shannon's theorem.

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It's an effect of the sampling. This mirrors your signal with respect to $f_S$/2 and its multiples.