Sampling rate
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The sampling rate, sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is 1/s. The inverse of the sampling frequency is the sampling period or sampling interval, which is the time between samples.[1]
The concept of sampling frequency can only be applied to samplers in which samples are taken periodically. Some samplers may sample at a non-periodic rate.
The common notation for sampling frequency is fs which stands for frequency (subscript) sampled.
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[edit] Sampling theorem
The Nyquist–Shannon sampling theorem states that perfect reconstruction of a signal is possible when the sampling frequency is greater than twice the maximum frequency of the signal being sampled,[2] or equivalently, when the Nyquist frequency (half the sample rate) exceeds the highest frequency of the signal being sampled. If lower sampling rates are used, the original signal's information may not be completely recoverable from the sampled signal.
For example, if a signal has an upper band limit of 100 Hz, a sampling frequency greater than 200 Hz will avoid aliasing and allow theoretically perfect reconstruction.
[edit] Oversampling
In some cases, it is desirable to have a sampling frequency more than twice the desired system bandwidth so that a digital filter can be used in exchange for a weaker analog anti-aliasing filter. This process is known as oversampling.[3] The requirements for the Nyquist rate to hold is that the signal to be reconstructed is to be sinusoidal. It is a common error to interpret Nyquist theorem that with a sampling frequency of twice that of the original signal is enough for perfect reconstruction. At least additional understanding of Fourier series representation of a given signal would be required to make the Nyquist criteria valid. A safer interpretation would be that IF the signal is a sinusoid the Nyquist criteria will hold. This means that if a given signal can be represented by a Fourier series the applicable Nyquist rate would be twice the maximum frequency of the highest sinusoidal component of the signal as described by its Fourier series.
[edit] Undersampling
Conversely, one may sample below the Nyquist rate. For a baseband signal (one that has components from 0 to the Nyquist rate), this introduces aliasing, but for a passband signal (one that does not have low frequency components), there are no low frequency signals for the aliases of high frequency signals to collide with, and thus one can sample a high frequency (but narrow bandwidth) signal at a much lower sample rate than the Nyquist rate.
[edit] Video systems
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In digital video, the temporal sampling rate is defined the frame/field rate, rather than the notional pixel clock. 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.
When analog video is converted to digital video, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along scan lines. Some common pixel sampling rates are:
Spatial sampling in the other direction is determined by the spacing of scan lines in the raster. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.
Spatial aliasing of high-frequency luma or chroma video components shows up as a moiré pattern.
[edit] See also
[edit] References
- ^ Martin H. Weik (1996). Communications Standard Dictionary. Springer. ISBN 0412083914. http://books.google.com/books?id=ND2c1uq53TIC&pg=PA866&ots=jyC7vyPLLQ&dq=%22sampling+rate%22+frequency+period&sig=40Pw5vlPE-hXuM4-Rh3lpONQ6g4.
- ^ C. E. Shannon, "Communication in the presence of noise", Proc. Institute of Radio Engineers, vol. 37, no.1, pp. 10–21, Jan. 1949. Reprint as classic paper in: Proc. IEEE, Vol. 86, No. 2, (Feb 1998)
- ^ William Morris Hartmann (1997). Signals, Sound, and Sensation. Springer. ISBN 1563962837. http://books.google.com/books?id=3N72rIoTHiEC&pg=PA485&ots=GT7aaJK5vq&dq=over-sampling+digital-filter+audio&sig=0ZvXTWSZNb0E1Ugm0_qoF8z-Z7E.
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