I am reading "Digital Signal Processing" - Proakis and often read that sampling guarantees periodicity (not exact as read)
But I wonder how sampling aperiodic signal will result in periodic repetitions of the aperiodic signal?
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sampling guarantees periodicity
Not exactly. Sampling in one domain guarantees periodicity in the other domain. So sampling in time creates a periodic spectrum and sampling in frequency creates a periodic time signal. Or the other one around: a periodic time signal has a discrete spectrum and a periodic spectrum has a discrete time signal.
That's why there are four different "types" of Fourier Transform. One for each permutations of continuous vs discrete in each domain. See for example http://fourier.eng.hmc.edu/e101/lectures/handout4/node3.html or https://www.dspguide.com/ch8/1.htm