signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...

, the Nyquist frequency (or folding frequency), named after

Harry Nyquist Harry Nyquist (, ; February 7, 1889 – April 4, 1976) was a Swedish-American physicist and electronic engineer who made important contributions to communication theory. Personal life Nyquist was born in the village Nilsby of the parish Stora Ki ...

, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of

cycles per second The cycle per second is a once-common English name for the unit of frequency now known as the hertz (Hz). The plural form was typically used, often written cycles per second, cycles/second, c.p.s., c/s, or, ambiguously, just cycles (Cy./Cyc.). T ...

( Hz), its value is one-half of the

sampling rate In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or s ...

(samples per second). When the highest frequency (

bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...

) of a signal is less than the Nyquist frequency of the sampler, the resulting

discrete-time In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "po ...

sequence is said to be free of the distortion known as

aliasing In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when ...

, and the corresponding sample rate is said to be above the

Nyquist rate In signal processing, the Nyquist rate, named after Harry Nyquist, is a value (in units of samples per second or hertz, Hz) equal to twice the highest frequency ( bandwidth) of a given function or signal. When the function is digitized at a hi ...

for that particular signal. In a typical application of sampling, one first chooses the highest frequency to be preserved and recreated, based on the expected content (voice, music, etc.) and desired fidelity. Then one inserts an

anti-aliasing filter An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruct ...

ahead of the sampler. Its job is to attenuate the frequencies above that limit. Finally, based on the characteristics of the filter, one chooses a sample rate (and corresponding Nyquist frequency) that will provide an acceptably small amount of

. In applications where the sample rate is pre-determined, the filter is chosen based on the Nyquist frequency, rather than vice versa. For example, audio CDs have a sampling rate of 44100 samples/sec. The Nyquist frequency is therefore 22050 Hz. The anti-aliasing filter must adequately suppress any higher frequencies but negligibly affect the frequencies within the human

hearing range Hearing range describes the range of frequencies that can be heard by humans or other animals, though it can also refer to the range of levels. The human range is commonly given as 20 to 20,000 Hz, although there is considerable variati ...

; a filter that preserves 0–20 kHz is more than adequate for this.

Folding frequency

In this example, is the sampling rate, and is the corresponding Nyquist frequency. The black dot plotted at represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that would produce the same set of samples as the actual sinusoid that was sampled. Undersampling of the sinusoid at is what allows there to be a lower-frequency alias. If the true frequency were , there would still be aliases at 0.6, 1.4, 1.6, etc. The red lines depict the paths ( loci) of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between and ). No matter what function we choose to change the amplitude vs frequency, the graph will exhibit symmetry between 0 and This symmetry is commonly referred to as folding, and another name for (the Nyquist frequency) is folding frequency.

Other meanings

Early uses of the term ''Nyquist frequency'', such as those cited above, are all consistent with the definition presented in this article. Some later publications, including some respectable textbooks, call twice the signal bandwidth the Nyquist frequency; this is a distinctly minority usage, and the frequency at twice the signal bandwidth is otherwise commonly referred to as the

Notes

References

{{DSP Digital signal processing