sampling theorem
The greyvalues of digitized one or twodimensional signals are typically generated by an analoguetodigital 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 bandlimited analogue signal ${x}_{a}(t)$, i.e. a signal in a finite frequency band (e.g. between 0 and BHz), can be completely reconstructed from its samples $x(n)=x(nT)$, if the sampling frequency is greater than $2B$ (the Nyquist rate); expressed in the , this that the sampling interval $T$ is at most $\frac{1}{2B}$ seconds. Undersampling can produce serious errors (aliasing) by introducing artifacts of low frequencies, both in onedimensional signals and in digital .
References

•
Originally from the Data Analysis Briefbook (http://rkb.home.cern.ch/rkb/titleA.htmlhttp://rkb.home.cern.ch/rkb/titleA.html)
Title  sampling theorem 

Canonical name  SamplingTheorem 
Date of creation  20130322 12:04:25 
Last modified on  20130322 12:04:25 
Owner  akrowne (2) 
Last modified by  akrowne (2) 
Numerical id  8 
Author  akrowne (2) 
Entry type  Theorem 
Classification  msc 94A20 
Synonym  Nyquist’s theorem 