In many applications such as audio applications, it is useful to represent a signal in terms of sample values taken at appropriately spaced intervals. The signal can be reconstructed from the sampled waveform by passing it through an ideal low pass filter. In order to ensure a distortionless reconstruction, the original signal must be sampled at an appropriate rate as described by the sampling theorem.

The sampling theorem states that

If the sampling rate in any pulse modulation system exceeds twice the maximum signal frequency, the original signal can be reconstructed in the receiver with minimal distortion.

Sampling theorem is useful to determine the minimum sampling speeds in different application such as speech modulation. 

Sampling theorem limits the minimum sampling speed and below this speed distortion takes place. For example, A 300 to 3400 Hz audio signal is sampled at 8000 samples per second then the resulting reconstructed signal is free from sampling error.

Sampling Theorem

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