Nyquist–Shannon sampling theorem - Wikipedia

Abstraction: Fundamental theorem defining minimum sampling rate for lossless reconstruction

Key points:

• A band-limited signal with maximum frequency B Hz can be perfectly reconstructed from samples taken at a rate of more than 2B samples/second (the Nyquist rate); the sample rate must be strictly greater than twice the bandwidth.
• Reconstruction uses the Whittaker–Shannon interpolation formula: sum of sinc functions centered at each sample, scaled by sample values.
• Aliasing occurs when the sampling rate is below the Nyquist rate; adjacent spectral copies overlap and frequency components above fs/2 become indistinguishable from lower-frequency aliases.
• For bandpass (non-baseband) signals, the minimum required sample rate equals twice the signal bandwidth, not twice the highest frequency (e.g., 100-102 MHz FM can be sampled at 4 MHz, not 204 MHz).
• Compressed sensing allows sub-Nyquist reconstruction when signals are sparse in some domain, converting the reconstruction to a linear optimization problem.
• The theorem was independently discovered by Whittaker (1915), Kotelnikov (1933), Shannon (1949), and others; "Nyquist" was attached historically though his contribution was the signaling rate, not the sampling theorem per se.

Connections: Harry Nyquist · Claude Shannon · Sampling Theorem · Signal Processing · Aliasing

Source: http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem