# Sampling theorem

Nyquist–Shannon Sampling Theorem

The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal(for example, a function of continuous time or space) into a numeric sequence (a function of discrete time or space).

Sampling theorem, which in essence shows that a band-limited analog signal can be reconstructed perfectly from an infinite sequence of samples if the sample rate exceeds 2B samples per second. B is the highest frequency in the original signal. If the signal contains components at exactly B hertz, then samples spaced 1/(2B) seconds do NOT completely determine the signal.

E.g. 20,000 Hertz into this formula will not be reconstructed perfectly at anything less than 0.00003 seconds per sample. Recording at a sample rate of 48kHz is sampling at 0.00002 seconds per sample, hence for situations like recording dialogue where the highest frequency for normal conversation is below 20kHz (because we can't hear higher anyway).

Possibly Useful Drawing of a 2hz sine wave Uses in recording effects. If you wanted to have flexibility to manipulate then you can record at 192kHz and then the spacing is 1 sample every 0.0000052083 of a second, this is useful for slowing down sounds as more samples will spread evenly and more effectively than less samples. This is again like most theories based on a perfect world and so is an approximate in our not so perfect world. So there you have Sampling theorem.