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Concept# Nyquist rate

Summary

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 higher sample rate (see ), the resulting discrete-time sequence is said to be free of the distortion known as aliasing. Conversely, for a given sample-rate the corresponding Nyquist frequency in Hz is one-half the sample-rate. Note that the Nyquist rate is a property of a continuous-time signal, whereas Nyquist frequency is a property of a discrete-time system.
The term Nyquist rate is also used in a different context with units of symbols per second, which is actually the field in which Harry Nyquist was working. In that context it is an upper bound for the symbol rate across a bandwidth-limited baseband channel such as a telegraph line or passband channel such as a limited radio frequency band or a frequency division multiplex channel.
When a continuous function, is sampled at a constant rate, samples/second, there is always an unlimited number of other continuous functions that fit the same set of samples. But only one of them is bandlimited to cycles/second (hertz), which means that its Fourier transform, is for all 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. It follows that if the original function, is bandlimited to which is called the Nyquist criterion, then it is the one unique function the interpolation algorithms are approximating. In terms of a function's own bandwidth as depicted here, the Nyquist criterion is often stated as And is called the Nyquist rate for functions with bandwidth When the Nyquist criterion is not met say, a condition called aliasing occurs, which results in some inevitable differences between and a reconstructed function that has less bandwidth. In most cases, the differences are viewed as distortion.

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Sampling (signal processing)

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 space; this definition differs from the term's usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

Aliasing

In signal processing and related disciplines, aliasing is the overlapping of frequency components resulting from a sample rate below the Nyquist frequency. This overlap results in distortion or artifacts when the signal is reconstructed from samples which causes the reconstructed signal to differ from the original continuous signal. Aliasing that occurs in signals sampled in time, for instance in digital audio or the stroboscopic effect, is referred to as temporal aliasing. Aliasing in spatially sampled signals (e.

Nyquist frequency

In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal 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 period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.

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