Sampling

Sampling represents a continuous-time or continuous-space signal by measuring it at discrete intervals. The sampling pattern and rate determine which variations the measurements can preserve.

Sampling theorem: A result specifying conditions under which a band-limited signal can be reconstructed exactly from regularly spaced samples. It sets the minimum sampling rate needed to preserve a signal's highest frequency.
Continuous signal: A signal defined across a continuous range of time or space, rather than only at discrete points. Sampling starts with a signal whose values exist between measurement instants.
Digital audio: Sound represented as numerical measurements of acoustic pressure taken at discrete times. Audio systems sample sound waves to store, process, and reproduce them.
Uniform sampling: Sampling at equal intervals of time or space. It is the standard pattern behind many sampling-rate and reconstruction results.
Nyquist frequency: Half the sampling rate; the highest frequency that can be represented without aliasing under ideal uniform sampling. It marks the frequency limit imposed by a chosen sampling rate.
Discrete-time signal: A sequence of values indexed at separate time points, whether or not those values are quantized. It is the representation produced when a time-varying signal is sampled.
Digital image: An image represented by discrete picture elements, each holding one or more measured or encoded values. A spatial sampling grid turns a continuous scene or image into pixels.
Nonuniform sampling: Sampling at unequal intervals or at points that do not form a regular grid. Its irregular timing changes the conditions and methods for signal reconstruction.
Aliasing: The misrepresentation of distinct frequencies or patterns as the same signal after sampling. Insufficient sampling makes higher-frequency variation appear as a different, lower-frequency pattern.
Quantization: The mapping of values from a continuous or large set of levels to a finite set of allowed levels. It follows sampling in many digital systems but changes amplitude precision, not sample timing.

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