# Nyquist frequency – Wikipedia

*by*Phil Tadros

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Most frequency of non-aliased element upon sampling

In signal processing, the **Nyquist frequency** (or **folding frequency**), named after Harry Nyquist, is a attribute of a sampler, which converts a steady operate or sign right into a discrete sequence. For a given sampling rate (*samples per second*), the Nyquist frequency *(cycles per second*) is the frequency whose cycle-length (or interval) is twice the interval between samples, thus *0.5 cycle/pattern*. For instance, audio CDs have a sampling fee of 44100 *samples/second*. At *0.5 cycle/pattern*, the corresponding Nyquist frequency is 22050 *cycles/second* (Hz). Conversely, the Nyquist fee for sampling a 22050 Hz sign is 44100 *samples/second*.^{[1]}^{[2]}^{[A]}

When the very best frequency (bandwidth) of a sign is lower than the Nyquist frequency of the sampler, the ensuing discrete-time sequence is alleged to be freed from the distortion referred to as aliasing, and the corresponding pattern fee is alleged to be above the Nyquist rate for that individual sign.^{[3]}^{[4]}

In a typical software of sampling, one first chooses the very best frequency to be preserved and recreated, primarily based on the anticipated content material (voice, music, and many others.) and desired constancy. Then one inserts an anti-aliasing filter forward of the sampler. Its job is to attenuate the frequencies above that restrict. Lastly, primarily based on the traits of the filter, one chooses a pattern fee (and corresponding Nyquist frequency) that can present an acceptably small quantity of aliasing. In functions the place the pattern fee is pre-determined (such because the CD fee), the filter is chosen primarily based on the Nyquist frequency, moderately than vice versa.

## Folding frequency[edit]

On this instance, *f*_{s} is the sampling fee, and 0.5 *cycle/pattern* × *f*_{s} is the corresponding Nyquist frequency. The black dot plotted at 0.6 *f*_{s} represents the amplitude and frequency of a sinusoidal operate whose frequency is 60% of the pattern fee. The opposite three dots point out the frequencies and amplitudes of three different sinusoids that might produce the identical set of samples because the precise sinusoid that was sampled. Undersampling of the sinusoid at 0.6 *f*_{s} is what permits there to be a lower-frequency alias. If the true frequency have been 0.4 *f*_{s}, there would nonetheless be aliases at 0.6, 1.4, 1.6, and many others.

The pink traces depict the paths (loci) of the 4 dots if we have been to regulate the frequency and amplitude of the sinusoid alongside the strong pink phase (between *f*_{s}/2 and *f*_{s}). It doesn’t matter what operate we select to vary the amplitude vs frequency, the graph will exhibit symmetry between 0 and *f*_{s}. This symmetry is usually known as **folding**, and one other title for *f*_{s}/2 (the Nyquist frequency) is **folding frequency**.^{[5]}

## Different meanings[edit]

Early makes use of of the time period *Nyquist frequency*, similar to these cited above, are all according to the definition offered on this article. Some later publications, together with some respectable textbooks, name twice the sign bandwidth the Nyquist frequency;^{[6]}^{[7]} it is a distinctly minority utilization, and the frequency at twice the sign bandwidth is in any other case generally known as the Nyquist rate.

**^**When the operate area is distance, as in a picture sampling system, the pattern fee is perhaps dots per inch and the corresponding Nyquist frequency can be in cycles per inch.

## References[edit]