Yes, the original signal will be accurately reproduced, provided it did not contain any frequencies at or above 1/2 the sampling rate (Nyquist). If you're looki

Yes, the original signal will be accurately reproduced, provided it did not contain any frequencies at or above 1/2 the sampling rate (Nyquist). If you're looking for some intuition, the restriction on input frequencies guarantees that the signal doesn't "change too fast" between samples. You don't lose any information simply because you make sure there's nothing in the signal you can't capture. All this assumes infinite measuring precision, which is of course incorrect - in reality, the limited number of discrete levels a signal can take in a digital system introduces noise, or more accurately distortion since the noise is correlated with the signal. We fix this with dither, and it's absolutely essential for a digital audio system - by adding a small amount of random noise, you decorrelate the noise from the signal (you can do even better with "noise shaping"). Here's an illustration from wiki showing how nasty quantization error is [1]. To understand dither, it's interesting to think of the limit case of infinite sampling rate but only two levels, low and high. You could actually still reproduce sound perfectly with this setup, albeit still with a frequency limit. What you do is add "high frequency" (higher than the signal) random noise before you measure "low" or "high". This makes the probability of measuring "low" or "high" depend on the exact signal level, rather than whether it's above or below 50%. With enough samples you get a "pulse density modulated" signal, which lingers on low for low values and vice versa [2]. This is equivalent to a continuous signal summed with some nasty, but high-frequency noise. Filter the high-frequency noise you added back out and voila (your ear will do the filtering in a pinch, which is how you can get analog sound out of digital stuff, like hard drives and GPIO pins). Basically: finite sampling rate, infinite precision - fine, we can squeeze the information into the precision. Infinite sampling rate, finite precision - still fine, we can squeeze the information into the time domain. Finite sampling rate and finite precision, i.e. the real world - there will be some error. [1] https://upload.wikimedia.org/wikipedia/commons/2/22/Quanterr.png https://upload.wikimedia.org/wikipedia/commons/2/22/Quanterr... [2] https://upload.wikimedia.org/wikipedia/commons/e/e7/Pulse_density_modulation.svg https://upload.wikimedia.org/wikipedia/commons/e/e7/Pulse_de...