# Shannon’s sampling theorem

The minimum sampling rate used with any system bears great importance. Only a finite number of samples can be taken at any time, and loss of information could result due to inadequate sampling frequency. Shannon’s sampling theorem establishes the theoretical basis for all the discrete sampling operations carried out on analog signals.

Shannon’s sampling theorem states that if a signal is sampled for all time at a rate more than twice the highest frequency, it can be exactly reconstructed from the samples. If sampling is done at a rate higher than twice the highest frequency, the aliases don’t overlap and the original signal can be recovered.

If sampling is done at a slower rate than twice the frequency, then aliases would overlap. Assuming the signal has a spectrum with frequency components extending from DC to a maximum frequency of fi Hz, Shannon’s sampling theorem states that the minimum possible sampling rate above which a bandpass signal can be recovered from the samples can be shown to be

fs > 2fi Hz