Sampling (information theory) - Definition

In information theory, sampling is the process of converting a continuous signal into a discrete signal.

Theoretical sampling

A theoretical/ideal sampler results from multiplying a continuous signal with a Dirac comb. The resulting signal is then a scaled Dirac comb. The discrete signal would then be the sequence of scale values

Realizable sampling

Realizable samplers are called analog to digital converters (A/D converter or ADC).

Distortion

Sampling distortion is introduced when the sampler is non-ideal. Several forms of distortion can be realized:

• Jitter: derivation from being sampled periodically
• Summing effect (for lack of a better term): when a sampler has a non-zero width in which the sample is taken.

This summing effect is readily noticeable in photography when the exposure is too long and creates a blur in the image. An ideal camera would have an exposure time of zero.

In a capacitor-based sample and hold circuit, the summing effect is introduced because the capacitor cannot instantly change voltage thus requiring the sample to have non-zero width.

List of sampling topics

Sampling theory:

• Nyquist-Shannon sampling theorem
• Nyquist-Shannon interpolation formula

Definitions:

• Continuous signal vs. Discrete signal
• Information theory
• Sample (signal)
• Sampling frequency

Sampling rates:

• Downsampling
• Upsampling
• Oversampling
• Undersampling

People:

• Harry Nyquist
• Claude E. Shannon