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@mattly You're right - it's not nothing. Essentially acquisition is an integration operation which is then averaged out - so the sample is an estimate of the value at a specific point. You trade the time inaccuracy for some value inaccuracy. Since the digital representation already has more value error than you're introducing, it is a fine trade off.

But the "at an instant" aspect of the sample is essential for DSP algo.s to produce correct results. This all flows from the Sampling Theorem.