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nyquist rate
In signal processing, the Nyquist rate, named after Harry Nyquist, is twice the bandwidth of a bandlimited function or a bandlimited channel. This term means two different things under two different circumstances:
# as a lower bound for the sample rate for alias-free signal sampling (not to be confused with the Nyquist frequency, which is half the sampling rate of a discrete-time system) and
# as 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.
==Nyquist rate relative to sampling==
When a continuous function, x(t), is sampled at a constant rate, fs ''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 ½ fs ''cycles/second'' (hertz),〔The factor of ½ has the units ''cycles/sample'' (see Sampling and Sampling theorem).〕 which means that its Fourier transform, X(f), is 0 for all |f| ≥ ½ fs. 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, x(t), is bandlimited to ½ fs, 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 (B), as depicted above, the Nyquist criterion is often stated as fs > 2B. And 2B is called the Nyquist rate for functions with bandwidth B. When the Nyquist criterion is not met (B > ½ fs), a condition called aliasing occurs, which results in some inevitable differences between x(t) and a reconstructed function that has less bandwidth. In most cases, the differences are viewed as distortion.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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