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A fluctuation in the time at which a signal is sampled produces an amplitude error proportional to its local time derivative. For a sinusoid, the characteristic fractional error grows with the product of frequency and timing uncertainty. Sampling-time uncertainty is distinct from uniform quantization error.

A smooth input probability density varying slowly on the scale of one conversion interval makes the fractional uniform quantization error approximately uniform. Large overall variance is not sufficient: discrete inputs aligned with conversion levels provide a counterexample. Clipping, coarse sampling and correlations between error and signal require separate analysis.

In the high-resolution quantization approximation, a smooth input distribution varies little across one conversion interval, so rounding to the nearest level gives an approximately uniform quantization error $ϵ\in [-\Delta V/2,\Delta V/2]$. ThereforeThe input must stay within the analogue-to-digital converter's range. A large standard deviation alone does not guarantee uniform quantization error: an input concentrated exactly on widely separated conversion levels has zero error. Truncation without a half-step correction also has a different mean and root mean square.

Uniform samples at $t_n=n/f_s$ cannot distinguish frequencies separated by integer multiples of $f_s$:For a real cosine, opposite frequencies also coincide. Thus an unknown high-frequency component can appear in the sampled record at its folded frequency $f_{\mathrm{alias}}\in [0,f_s/2]$. For example, 2 Hz and 8 Hz cosines give identical samples at 10 samples per second. This ambiguity is aliasing, rather than uniform quantization error.

The Nyquist–Shannon sampling theorem permits reconstruction of an ideally bandlimited function of bandwidth $B$ when $f_s>2B$. Use an analogue anti-aliasing filter before conversion and allow a transition band between the desired passband and the frequencies that fold into it. Sampling faster relaxes the filter requirement. Digital filtering after undersampling cannot separate already identical sample sequences. Finite observation time, clock jitter, noise and imperfect filter rejection impose further practical limits.