A cross-correlation is a mathematical operation that computes the similarity between two signals x(t) and y(t) as a function of a time lag τ applied to one signal: R_xy(τ) = ∫ x(t)·y*(t-τ) dt (continuous) or R_xy[τ] = Σ x[n]·y*[n-τ] (discrete). It operates by sliding one signal past another, computing an overlap integral or sum at each lag, producing a cross-correlogram that reveals delay, periodicity, and matching patterns. Persistence mechanism: algorithmic computation over discrete sample arrays or continuous functions, implemented via direct summation or FFT-based convolution. [formal: cross-correlation | substrate: behavior | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
cross-correlation
A cross-correlation is a mathematical operation that computes the similarity between two signals x(t) and y(t) as a function of a time lag τ applied to one signal: R_xy(τ) = ∫ x(t)·y*(t-τ) dt (continuous) or R_xy[τ] = Σ x[n]·y*[n-τ] (discr…
Definition
Why it is in scope
A human-made mathematical construct in signal processing and statistics: a measure of similarity between two signals as a function of time-lag applied to one of them. Built to persist as an algorithmic operation over discrete or continuous signals, enabling pattern matching, delay estimation, and template matching.
Names and aliases
- cross-correlationen · CANONICAL
Relations from this entry
- cmrw5yp7v001nkyo64adfdvitINSTANCE_OF →
Cross-correlation is a specific kind of correlation measuring similarity between two signals as a function of time lag. A competent speaker would call it 'a correlation method'. Pin sense: correlation as the general statistical measure of relationship between variables.
- cmrw5yp7v001nkyo64adfdvitDERIVED_FROM →
which-came-first: correlation (19th century statistics) predates cross-correlation (developed for signal processing, 20th century). Correlation is the general concept from which cross-correlation was derived as a specialized variant for comparing two distinct signals.
- cmsps9i0v06eejlssqrjcqyviINSTANCE_OF →
Cross-correlation is a specific signal processing technique that measures similarity between two signals as a function of displacement. It is a canonical instance of signal processing operations.
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Record identity
- Created
- Aug 12, 2026, 4:45 PM UTC
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- 948ec83e3b05cffe967f8dfe77d788a47ef9811e6b0c3700c55e3f8c0313aca1