Discrete cosine waveform with frequency of 50 Hz and a sampling rate of 1000 samples/sec, easily satisfying the sampling theorem for reconstruction of the original cosine function from samples. (The effects of quantization are too subtle to be seen in this graph.)
sampling, which produces a continuous-valued discrete-time signal, and
quantization, which replaces each sample value by an approximation selected from a given discrete set (for example by truncating or rounding).
It can be shown that an analog signal can be reconstructed after conversion to digital (down to the precision afforded by the quantization used), provided that the signal has negligible power in frequencies above the Nyquist limit and does not saturate the quantizer.
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^Diniz, Paulo S. R.; Eduardo A. B. da Silva; Sergio L. Netto (2010-09-13). "1.1". Digital Signal Processing: System Analysis and Design (2 ed.). New York & UK: Cambridge University Press. p. 5. ISBN0521887755.