sampling theorem

The sampling theorem states that a time function f(t), whose frequency spectrum lies in the frequency band 0 Hz to B Hz, is uniquely determined by its ordinates at equidistant points, provided these points are no further than 1/2B seconds apart.

According to the sampling theorem, the sampling rate must be at least twice that of the sampled signal in order to reproduce the original signal from the sampled voltage values. For example, if the signal to be sampled has a frequency of 500 kHz, then the sampling rate must be greater than 1 MHz. The sampling theorem, also known as the Nyquist sampling theorem, is fundamental to the application of information theory to continuous signals because it allows a continuous signal of finite duration to be represented by a finite number of degrees of freedom, i.e., also as a binary signal.

If the sampling rate is higher than the theorem states by a certain factor, it is called oversampling; the oversampling factor is called the oversampling ratio( OSR).