A convolution is a mathematical operation that combines two functions to produce a third, expressing how the shape of one is modified by the other. Parameters: (1) domain — continuous (integral form: ∫f(τ)g(t-τ)dτ) or discrete (summation form: Σf[k]g[n-k]); (2) interpretation — in signal processing it computes how an impulse-response warps an input signal; in probability it yields the distribution of the sum of independent random variables; in geometry it models morphological dilation/erosion; (3) commutativity — f*g = g*f holds for all standard convolution operations. [formal: convolutio | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
convolution
A convolution is a mathematical operation that combines two functions to produce a third, expressing how the shape of one is modified by the other. Parameters: (1) domain — continuous (integral form: ∫f(τ)g(t-τ)dτ) or discrete (summation f…
Definition
Why it is in scope
A human-made concept in mathematics and signal processing that models the combination of two functions to produce a third — specifically, how a signal's shape is transformed by a system's impulse response, and more broadly how one function's structure warps or filters another. Built to persist through integral and summation formulas, enabling analysis of linear systems, probability distributions, and spatial transformations.
Names and aliases
- convolutionen · CANONICAL
Relations from this entry
- cmr9uz3vv00elhcxfruyltnd4SERVES →
Convolution serves measurement: it is the fundamental operation for characterizing system responses through measured impulse responses and for extracting signal properties via matched-filter detection. Remove measurement as a goal and convolution's application in signal characterization loses its purpose. By design, convolution enables the measurement of system properties.
Relations to this entry
- cmsp757bx04cojlssckoi3vr7← DEPENDS_ON
Spectral leakage is caused by the convolution of the signal spectrum with the window function spectrum in the frequency domain. Remove convolution from the concept and spectral leakage ceases to operate — there is no mechanism for leakage without convolution. The removal test passes: without the convolution mechanism, the concept has no operational basis.
- cmspjtxbm05nkjlssyyotmh5n← DEPENDS_ON
Deconvolution is defined as the reverse of convolution. Remove the concept of convolution and deconvolution loses its entire meaning — there is no 'de-' (reverse) without the base operation. The deconvolution algorithm operates only within the convolution framework. Law 8 removal test: remove convolution and deconvolution stops operating.
- overlap-save← INSTANCE_OF
Overlap-save IS a specific kind of convolution method: it performs linear convolution via overlapping blocks in the frequency domain. A competent speaker would call overlap-save a convolution technique. Nearest kind: convolution (ACCEPTED).
Record identity
- Created
- Aug 11, 2026, 7:47 PM UTC
- Content hash
- 24438564371d01de989766d3fb96dd5a39a4024bf30213a941d788b86e9b4033