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sampling theorem
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(Theorem)
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Sampling Theorem
The greyvalues of digitized one- or two-dimensional signals are typically generated by an analogue-to-digital converter (ADC), by sampling a continuous signal at fixed intervals (e.g. in time), and quantizing (digitizing) the samples. The sampling (or point sampling) theorem states that a band-limited analogue signal  , i.e. a signal in a finite frequency band (e.g. between 0 and BHz), can be completely reconstructed from its samples
 , if the sampling frequency is greater than  (the Nyquist rate); expressed in the time domain, this means that the sampling interval  is at most
 seconds. Undersampling can produce serious errors (aliasing) by introducing artifacts of low frequencies, both in one-dimensional signals and in digital images.
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"sampling theorem" is owned by akrowne.
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| Other names: |
Nyquist's theorem |
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Cross-references: aliasing, band, finite, point, intervals, fixed, continuous, generated by
There are 3 references to this entry.
This is version 4 of sampling theorem, born on 2001-12-25, modified 2002-02-19.
Object id is 1143, canonical name is SamplingTheorem.
Accessed 6758 times total.
Classification:
| AMS MSC: | 94A20 (Information and communication, circuits :: Communication, information :: Sampling theory) |
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Pending Errata and Addenda
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![\includegraphics[scale=.5]{img988.eps}](http://images.planetmath.org:8080/cache/objects/1143/l2h/img6.png "\includegraphics[scale=.5]{img988.eps}")