convolution

noun

Etymology: Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Proto-Indo-European *welH-der. Proto-Italic *wolwō Latin volvō Latin convolvō Latin convolūtusbor. English -tion English convolution Borrowed from Latin convolutus (“to roll together”), past participle of convolvere, from con- + volvere (“to roll”), with the suffix -tion. Equivalent to convolute + -ion. The mathematical sense is a semantic calque from Faltung.

1. A twist or fold.
2. Any of the folds on the surface of the brain.
3. The shape of something rotating; a vortex.
4. The state or condition of being convoluted.
5. A mathematical operation on two functions that produces a third that expresses how the shape of one is modified by the other; the integral of the product of the two functions after one is reflected about the y-axis and shifted along the x-axis.

   “1934, Aurel Wintner, The proper method in dealing with distribution functions and their convolutions (“Faltungen”) is the method of Fourier transforms, first applied systematically by Levy in his book on the calculus of probability.”

   “Linear convolution is one of the most frequent computations carried out in digital signal processing (DSP).”

6. A function which maps a tuple of sequences into a sequence of tuples.
7. One 360° turn in a spring or similar helix.