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The Nyquist rate, named after the Nyquist-Shannon sampling theorem, is immediately below the minimum theoretical sampling rate that will fully describe a given band-limited signal, enabling its faithful reconstruction from the samples. If the signal's largest frequency component is , the Nyquist rate is and the sampling rate must be something larger than .The Nyquist rate also represents the maximum rate at which ideal pulses can be sent over an ideal low pass channel; for instance, if the channel passes all frequencies at or below Hz, then you can transmit pulses per second.
If a signal is sampled at a frequency , any information it contains at or above a frequency of cannot be recovered from the sampled data. The frequency is known as the Nyquist frequency. The higher-frequency components are not lost; instead, they are merged with the lower-frequency components and become indistinguishable from the lower-frequency components. This effect is known as aliasing or folding. The use of an anti-aliasing filter may be necessary to remove those higher-frequency components before the signal is sampled thus preventing the aliasing.
As an example, audio CDs generally have a sampling frequency of 44100 Hertz (Hz). The Nyquist frequency tells us that no audio CD can reproduce frequencies as high or higher than 22050 Hz if the lowest frequency to be sampled is 0 Hz.
Due to quantization errors introduced by the sampling process, imperfect pulses, and imperfect anti-aliasing filters in real systems, the actual sampling rate required to reconstruct the original signal will be somewhat higher than the Nyquist rate (or twice the Nyquist frequency).
Digital signal processing
