Sampling Theorem
The Nyquist–Shannon sampling theorem states that perfect reconstruction of a signal is possible when the sampling frequency is greater than twice the maximum frequency of the signal being sampled, or equivalently, when the Nyquist frequency (half the sample rate) exceeds the highest frequency of the signal being sampled. If lower sampling rates are used, the original signal's information may not be completely recoverable from the sampled signal. For example, if a signal has an upper band limit of 100 Hz, a sampling frequency greater than 200 Hz will avoid aliasing and would theoretically allow perfect reconstruction.
The full range of human hearing is between 20 Hz and 20 kHz. The minimum sampling rate that satisfies the sampling theorem for this full bandwidth is 40 kHz. The 44.1 kHz sampling rate used for Compact Disc was chosen for this and other technical reasons.
Read more about this topic: Sampling Rate
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)