convolutionとは 意味・読み方・使い方

語源

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.

発音

• 韻: -uːʃən

名詞

convolution (countable and uncountable, plural convolutions)

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. (mathematics, functional analysis) 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.

   Coordinate term: deconvolution

   • 1934, Aurel Wintner, (Can we date this quote by Wintner and provide title, author’s full name, and other details?)

     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.

   • 1997, Richard Tolimieri, Myoung An, Chao Lu, Algorithms for Discrete Fourier Transform and Convolution, 2nd edition, Springer, page 101:

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

   • 1994, Semen B. Yakubovich, Yurii F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer, page 183:

     In Chapter 11 we considered ${\displaystyle H}$-convolutions of generalized ${\displaystyle H}$-transforms. These convolutions are bilinear, commutative and associative operations […] .

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

使用する際の注意点

• (functional analysis): The term refers to both the result function and to the process of computing it.

派生語

関連する語

• convolve
• convolute
• convoluted

参考

• autocorrelation
• cross-correlation

参照

• “convolution”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• William Dwight Whitney, Benjamin E[li] Smith, editors (1911), “convolution”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.

Further reading

• Convolution (disambiguation) on Wikipedia.Wikipedia
• Convolution (computer science) on Wikipedia.Wikipedia
• Convolution on Wolfram MathWorld
• Convolution of functions on Encyclopedia of Mathematics