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Sampling continuous domains on discrete grids

A computer often represents a quantity that varies continuously over time or space by storing values only at separated locations. This process is sampling.

The sampling interval is the spacing between neighboring measurements. Samples may lie along a time axis, along a spatial line or on a multidimensional grid.

Smaller spacing records finer variation but requires more samples. The stored values say what was measured at the chosen locations; they do not directly specify what happened between them.

Reconstructing a continuous quantity from discrete samples therefore requires assumptions about how rapidly the original quantity can vary and a rule for estimating values between samples.

The same abstraction appears in many domains: digital audio samples a waveform over time, a raster image samples light over space, and numerical methods sample continuous fields on computational grids.

Sampling is distinct from quantization, which restricts the values themselves to a finite or discrete set.