# Sampling Theorem

## Sampling

In digital circuits, the data is sampled for a particular interval of time since the communication channels are many a time shared by a number of variables, The main purpose of signal sampling is the efficient use of the data processing and the data transmission units. The sampling operation is shown in fig 1.1. This shows that an analog signal and a train of periodic sampling signal whose ‘on’ time is extremely short as compared with the total period of the signal.

The result of the sampling process is identical to multiplying the analog signal by a train of pulses of unit magnitude. This preserves the amplitude of the analog signal in the modulation envelope of the pulses.

The sampling theorem states that if the highest frequency content in the input signal is fh Hz, then the input signal can be recovered without distortion if it is sampled at a rate of at least 2fh, samples per second. This is called the Nyquist rate. However, in practice, it is necessary to sample at least 5fh samples per second in order to reduce the effects of noise and non-sinusoidal filters. The sample and hold circuit acts as a low pass filter with a cut-off frequency fc=fs/2 where fs-sampling frequency.