# 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 $x_{a}(t)$, 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 one-dimensional 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 SamplingTheorem 2013-03-22 12:04:25 2013-03-22 12:04:25 akrowne (2) akrowne (2) 8 akrowne (2) Theorem msc 94A20 Nyquist’s theorem