"By contrast, the waveform reconstruction process – digital-to-analogue conversion – is not so simple. In an ideal world it would be achieved by generating an impulse of appropriate amplitude for each sampling point and passing the train of regularly spaced impulses through an ideal low-pass filter with its passband upper edge set to half the sampling rate. The impulse response of such a filter is the sinc function, so each impulse would generate a sinc waveform of the necessary amplitude, and the train of sinc functions would sum to recreate the original waveform.
This is illustrated in Fig 2, which shows six successive sinc functions of different amplitude and their sum (the black trace). Each sinc function contributes nothing to the summed signal amplitude at other sampling points, but does contribute to the waveform between the sampling points. It’s a common misunderstanding of sampling to suppose that the waveform between sampling points is unknowable but that is not true – provided that the input signal is bandlimited and sampled at least twice as fast as its highest component frequency, as required by the Shannon sampling process. In that case the waveform between sampling points can be reconstructed unambiguously. Importantly, the wave shape depends not just on the value of nearby samples but, ultimately, on the pattern of samples throughout the sampled signal" [1]
[1] https://drive.google.com/open?id=1QhJo_Rh8sQsItFvJ1g-MnNlg9p...
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