Shannon's sampling theorem

(Claude E. Shannon, born 1916, American mathematician), also known as the Nyquist criterion, a general "rule" for measurement of frequencies, stating that the measurement (sampling) frequency must be at least twice the maximum frequency to be measured. Whenever Shannon's sampling theorem is not fulfilled, aliasing occurs.

The theorem may be rephrased to say that if you want to measure the frequency of a repetitive event by sampling (e.g. taking snapshots of) the event, then you have to sample the event at a frequency at least twice the frequency of the event itself. For example, to measure the rotational frequencies of the three hands of a watch, a collection of snapshots taken with a frequency of at least twice per minute would be needed.

In radiology, Shannon's sampling theorem must be considered in e.g. the analogue to digital converter ADC , where the analogue signal must be sampled (i.e. its amplitude measured) with a frequency at least twice the frequency of the analogue signal, and in pulsed Doppler applications, where the pulse repetition frequency PRF , which here is equal to the sampling frequency, must be at least twice the maximum Doppler frequency shift to be measured. (See also sample and hold unit)

HJS