In signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, the Nyquist rate, named after Harry Nyquist

Harry Nyquist

Harry Nyquist was an important contributor to information theory.-Personal life:...

, is two times the bandwidth of a bandlimited

Bandlimited

Bandlimiting is the limiting of a deterministic or stochastic signal's Fourier transform or power spectral density to zero above a certain finite frequency...

 signal or a bandlimited channel. This term is used to mean two different things under two different circumstances:

1. as a lower bound for the sample rate for alias-free signal sampling (not to be confused with the Nyquist frequency
   Nyquist frequency
   The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...
   
   , which is half the sampling rate of a discrete-time system) and
2. as an upper bound for the symbol rate
   Symbol rate
   In digital communications, symbol rate is the number of symbol changes made to the transmission medium per second using a digitally modulated signal or a line code. The Symbol rate is measured in baud or symbols/second. In the case of a line code, the symbol rate is the pulse rate in pulses/second...
   
    across a bandwidth-limited baseband
   Baseband
   In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...
   
    channel such as a telegraph line or passband
   Passband
   A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
   
    channel such as a limited radio frequency band or a frequency division multiplex channel.

The Nyquist rate is the minimum sampling rate required to avoid aliasing

Aliasing

In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

, equal to twice the highest frequency contained within the signal.


where is the highest frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 at which the signal can have nonzero energy.

To avoid aliasing, the sampling rate must exceed the Nyquist rate:


A signal whose positive-frequency range of significant energy is (0, B), as depicted above, is called baseband or lowpass

Baseband

In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...

.