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Fig 1: 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). In signal processing, the Nyquist rate, named after Harry Nyquist, is a value equal to twice the highest frequency of a given function or signal
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 image sampling frequency is the repetition rate of the sensor integration period. Since the integration period may be significantly shorter than the time between repetitions, the sampling frequency can be different from the inverse of the sample time: 50 Hz – PAL video; 60 / 1.001 Hz ~= 59.94 Hz – NTSC video
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:
This Fourier series (in frequency) is a continuous periodic function, whose periodicity is the sampling frequency /. The subscript 1 / T {\displaystyle 1/T} distinguishes it from the continuous Fourier transform S ( f ) {\displaystyle S(f)} , and from the angular frequency form of the DTFT.
Principally, the samplling rate had to be at least double the maximal frequency carried (as per the Nyquist–Shannon sampling theorem) — at least 40 kHz to roughly cover all human-audible frequencies without aliasing distortion. [1] [2] The sampling rates under consideration ranged between 45 kHz and 60 kHz.
44,100 Hz, a customary rate used to sample audible frequencies is based on the limits of human hearing and the sampling theorem; Balian–Low theorem, a similar theoretical lower bound on sampling rates, but which applies to time–frequency transforms
The selection of the sample rate was based primarily on the need to reproduce the audible frequency range of 20–20,000 Hz (20 kHz). The Nyquist–Shannon sampling theorem states that a sampling rate of more than twice the maximum frequency of the signal to be recorded is needed, resulting in a required rate of greater than 40 kHz.