# Nyquist rate

Nyquist sampling rateNyquist limitNyquistNyquist criteriaNyquist intervalNyquist lawNyquist rate (relative to sampling)Nyquist sampling criteria
In signal processing, the Nyquist rate, named after Harry Nyquist, is twice the bandwidth of a bandlimited function or a bandlimited channel.wikipedia
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### Bandwidth (signal processing)

bandwidthbandwidthssignal bandwidth
In terms of a function's own bandwidth (B), as depicted above, the Nyquist criterion is often stated as f s > 2B.
In the context of, for example, the sampling theorem and Nyquist sampling rate, bandwidth typically refers to baseband bandwidth.

### Aliasing

aliasaliasedtemporal aliasing
And 2B is called the Nyquist rate for functions with bandwidth B. When the Nyquist criterion is not met (B > ½ f s ), a condition called aliasing occurs, which results in some inevitable differences between x(t) and a reconstructed function that has less bandwidth.
See Sampling (signal processing), Nyquist rate (relative to sampling), and Filter bank.

### Nyquist frequency

Nyquist limitNyquistN/2 different frequencies
The Nyquist frequency should not be confused with the Nyquist rate, the latter is the minimum sampling rate that satisfies the Nyquist sampling criterion for a given signal or family of signals.

### Symbol rate

symbolbaud rateSR
The maximum baud rate or pulse rate for a base band channel is called the Nyquist rate, and is double the bandwidth (double the cut-off frequency).

### Harry Nyquist

NyquistNyquist, Harry
Long before Harry Nyquist had his name associated with sampling, the term Nyquist rate was used differently, with a meaning closer to what Nyquist actually studied.

### Bandlimiting

bandlimitedband-limitedband limited
But only one of them is bandlimited to ½ f s cycles/second (hertz), which means that its Fourier transform, X(f), is 0 for all |f| ≥ ½ f s. The mathematical algorithms that are typically used to recreate a continuous function from samples create arbitrarily good approximations to this theoretical, but infinitely long, function.
This minimum sampling rate is called the Nyquist rate.

### Undersampling

bandpass samplingundersampled
For a more general discussion, see bandpass sampling.
In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal.

### Nyquist–Shannon sampling theorem

sampling theoremNyquist-Shannon sampling theoremNyquist theorem
Shannon used Nyquist's approach when he proved the sampling theorem in 1948, but Nyquist did not work on sampling per se.
The threshold 2B is called the Nyquist rate and is an attribute of the continuous-time input x(t) to be sampled.

### Sampling (signal processing)

sampling ratesamplingsample rate
When a bandpass signal is sampled slower than its Nyquist rate, the samples are indistinguishable from samples of a low-frequency alias of the high-frequency signal.

### Signal processing

signal analysissignalsignal processor

### Discrete time and continuous time

discrete timediscrete-timecontinuous-time

### Baseband

baseband signalbase bandcellular baseband
Figure 2 depicts a type of function called baseband or lowpass, because its positive-frequency range of significant energy is [0, B).

### Electrical telegraph

electric telegraphtelegraphtelegraph line

### Passband

pass bandpass-bandpassband signal

### Frequency-division multiplexing

frequency division multiplexingFDMfrequency division multiplex

### Hertz

MHzkHzHz
But only one of them is bandlimited to ½ f s cycles/second (hertz), which means that its Fourier transform, X(f), is 0 for all |f| ≥ ½ f s. The mathematical algorithms that are typically used to recreate a continuous function from samples create arbitrarily good approximations to this theoretical, but infinitely long, function.

### Fourier transform

continuous Fourier transformFourierFourier transforms
But only one of them is bandlimited to ½ f s cycles/second (hertz), which means that its Fourier transform, X(f), is 0 for all |f| ≥ ½ f s. The mathematical algorithms that are typically used to recreate a continuous function from samples create arbitrarily good approximations to this theoretical, but infinitely long, function.

### Band-pass filter

bandpass filterbandpassband-pass
When instead, the frequency range is (A, A+B), for some A > B, it is called bandpass, and a common desire (for various reasons) is to convert it to baseband.

### Heterodyne

heterodyningHeterodyne detectionfrequency shifting
One way to do that is frequency-mixing (heterodyne) the bandpass function down to the frequency range (0, B).

### Harold Stephen Black

Harold BlackHarold S. BlackBlack
Quoting Harold S. Black's 1953 book Modulation Theory, in the section Nyquist Interval of the opening chapter Historical Background:

### Oxford English Dictionary

OEDOxford DictionaryThe Oxford English Dictionary
According to the OED, Black's statement regarding 2B may be the origin of the term Nyquist rate.

### Oversampling

oversampledoverachievingoversample
In signal processing, oversampling is the process of sampling a signal at a sampling frequency significantly higher than the Nyquist rate.

### Oscilloscope types

sampling oscilloscope
When not using equivalent-time sampling, the sampling frequency should be higher than the Nyquist rate which is double the frequency of the highest-frequency component of the observed signal, otherwise aliasing occurs.

### Spectral efficiency

system spectral efficiencylink spectral efficiencySpectral efficiency comparison table
An upper bound for the attainable modulation efficiency is given by the Nyquist rate or Hartley's law as follows: For a signaling alphabet with M alternative symbols, each symbol represents N = log 2 M bits.