# 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.