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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 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second .
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 [ 2 ] or passband channel such as a limited radio frequency band ...
English: This is a typical example of Nyquist frequency and rate. They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth). They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth).
When is normalized with reference to the sampling rate as ′ =, the normalized Nyquist angular frequency is π radians/sample. The following table shows examples of normalized frequency for f = 1 {\displaystyle f=1} kHz , f s = 44100 {\displaystyle f_{s}=44100} samples/second (often denoted by 44.1 kHz ), and 4 normalization conventions:
The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at four times that rate requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter a transition band of 300 Hz ((f s /2) − B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz. Achieving an ...
A lower value of n will also lead to a useful sampling rate. For example, using n = 4, the FM band spectrum fits easily between 1.5 and 2.0 times the sampling rate, for a sampling rate near 56 MHz (multiples of the Nyquist frequency being 28, 56, 84, 112, etc.). See the illustrations at the right.
The bandwidth provided by the 44,100 Hz sampling frequency used by the standard for audio CDs is sufficiently wide to cover the entire human hearing range, which roughly extends from 20 Hz to 20 kHz. [ 2 ] : 108 Professional digital recorders may record higher frequencies, while some consumer and telecommunications systems record a more ...
A signal may be intentionally sampled at a higher rate to reduce the requirements and distortion of the anti-alias filter. For example, compare CD audio with high-resolution audio. CD audio filters the signal to a passband edge of 20 kHz, with a stopband Nyquist frequency of 22.05 kHz and sample rate of 44.1 kHz.