Nyquist frequency

In telecommunication, the Nyquist rate is the minimum theoretical sampling rate that fully describes a given band-limited signal, i.e., enables its faithful reconstruction from the samples. If the signal's largest frequency component is f₀, the Nyquist rate is 2f₀. Conversely, for a sampling rate f, the maximum frequency f/2 that can be reconstructed is called the Nyquist frequency.

If a signal is sampled at a frequency f, any information it contains above a frequency of f/2 cannot be reliably recovered from the sampled data. The frequency f/2 is known as the Nyquist frequency, in reference to the Nyquist-Shannon sampling theorem. The higher-frequency components are not lost, but are merged with the lower-frequency components, from which they cannot be separated. This effect is known as aliasing.

For example, an audio CD with a sampling frequency of 44100 Hz cannot reproduce frequencies higher than 22050 Hz if the lowest frequency to be sampled is 0 Hz.

Note 1: The actual sampling rate required to reconstruct the original signal will be somewhat higher than the Nyquist frequency, because of quantization errors introduced by the sampling process.

Note 2: The Nyquist rate is also the maximum rate that ideal pulses can be sent over an ideal low pass channel - ie, if the channel passes all frequencies at or below W (in Hz), you can transmit 2W pulses/second. As in Note 1, the actual maximum transmission rate is somewhat lower due to the imperfect pulses and filters used in real systems.