See convolution in All languages combined, or Wiktionary
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a vortex." ], "id": "en-convolution-en-noun-yoYEuKOO", "links": [ [ "rotating", "rotating" ], [ "vortex", "vortex" ] ], "tags": [ "countable", "uncountable" ], "translations": [ { "_dis1": "0 7 60 4 17 7 4", "code": "bg", "lang": "Bulgarian", "roman": "vitka", "sense": "shape of something rotating; a vortex — see also vortex", "tags": [ "feminine" ], "word": "витка" }, { "_dis1": "0 7 60 4 17 7 4", "code": "fi", "lang": "Finnish", "sense": "shape of something rotating; a vortex — see also vortex", "word": "kierre" } ] }, { "categories": [ { "_dis": "2 26 9 10 22 15 15", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "The state or condition of being convoluted." ], "id": "en-convolution-en-noun-8K-SjUYX", "links": [ [ "convoluted", "convoluted" ] ], "tags": [ "countable", "uncountable" ], "translations": [ { "_dis1": "0 0 4 89 3 2 1", "code": "fi", "lang": "Finnish", "sense": "state or condition of being convoluted", "word": "kiertyminen" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Functional analysis", "orig": "en:Functional analysis", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "3 28 7 9 18 12 24", "kind": "other", "name": "Terms with Bulgarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 26 9 10 22 15 15", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 27 8 9 20 12 23", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" } ], "examples": [ { "text": "1934, Aurel Wintner,\nThe 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." }, { "ref": "1997, Richard Tolimieri, Myoung An, Chao Lu, Algorithms for Discrete Fourier Transform and Convolution, 2nd edition, Springer, page 101:", "text": "Linear convolution is one of the most frequent computations carried out in digital signal processing (DSP).", "type": "quote" }, { "ref": "1994, Semen B. Yakubovich, Yurii F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer, page 183:", "text": "In Chapter 11 we considered H-convolutions of generalized H-transforms. These convolutions are bilinear, commutative and associative operations[…].", "type": "quote" } ], "glosses": [ "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." ], "id": "en-convolution-en-noun-~Wk~rI3T", "links": [ [ "mathematics", "mathematics" ], [ "functional analysis", "functional analysis" ], [ "integral", "integral" ] ], "qualifier": "functional analysis", "raw_glosses": [ "(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." ], "tags": [ "countable", "uncountable" ], "topics": [ "mathematics", "sciences" ], "translations": [ { "_dis1": "0 3 6 5 60 23 3", "code": "cmn", "lang": "Chinese Mandarin", "sense": "mathematics: mathematical operation on two functions", "word": "卷積" }, { "_dis1": "0 3 6 5 60 23 3", "code": "cmn", "lang": "Chinese Mandarin", "roman": "juǎnjī", "sense": "mathematics: mathematical operation on two functions", "word": "卷积" }, { "_dis1": "0 3 6 5 60 23 3", "code": "cmn", "lang": "Chinese Mandarin", "sense": "mathematics: mathematical operation on two functions", "word": "褶積" }, { "_dis1": "0 3 6 5 60 23 3", "code": "cmn", "lang": "Chinese Mandarin", "roman": "zhějī", "sense": "mathematics: mathematical operation on two functions", "word": "褶积" }, { "_dis1": "0 3 6 5 60 23 3", "code": "cs", "lang": "Czech", "sense": "mathematics: mathematical operation on two functions", "tags": [ "feminine" ], "word": "konvoluce" }, { "_dis1": "0 3 6 5 60 23 3", "code": "hu", "lang": "Hungarian", "sense": "mathematics: mathematical operation on two functions", "word": "konvolúció" }, { "_dis1": "0 3 6 5 60 23 3", "code": "is", "lang": "Icelandic", "sense": "mathematics: mathematical operation on two functions", "tags": [ "feminine" ], "word": "földun" }, { "_dis1": "0 3 6 5 60 23 3", "code": "it", "lang": "Italian", "sense": "mathematics: mathematical operation on two functions", "tags": [ "feminine" ], "word": "convoluzione" }, { "_dis1": "0 3 6 5 60 23 3", "code": "ckb", "lang": "Central Kurdish", "roman": "lûl", "sense": "mathematics: mathematical operation on two functions", "word": "لوول" }, { "_dis1": "0 3 6 5 60 23 3", "code": "ckb", "lang": "Central Kurdish", "roman": "pêç", "sense": "mathematics: mathematical operation on two functions", "word": "پێچ" }, { "_dis1": "0 3 6 5 60 23 3", "code": "pl", "lang": "Polish", "sense": "mathematics: mathematical operation on two functions", "tags": [ "masculine" ], "word": "splot" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Computing", "orig": "en:Computing", "parents": [ "Technology", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "3 28 7 9 18 12 24", "kind": "other", "name": "Terms with Bulgarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 26 9 10 22 15 15", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 19 12 9 20 26 12", "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 27 8 9 20 12 23", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "A function which maps a tuple of sequences into a sequence of tuples." ], "id": "en-convolution-en-noun-z3C6CZ7I", "links": [ [ "computing", "computing#Noun" ], [ "tuple", "tuple" ], [ "sequences", "sequences" ] ], "raw_glosses": [ "(computing) A function which maps a tuple of sequences into a sequence of tuples." ], "tags": [ "countable", "uncountable" ], "topics": [ "computing", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ] }, { "categories": [ { "_dis": "3 28 7 9 18 12 24", "kind": "other", "name": "Terms with Bulgarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 26 9 10 22 15 15", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" }, { "_dis": "2 27 8 9 20 12 23", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "One 360° turn in a spring or similar helix." ], "id": "en-convolution-en-noun-EVICXe76", "tags": [ "countable", "uncountable" ], "translations": [ { "_dis1": "0 1 1 1 2 1 94", "code": "fi", "lang": "Finnish", "sense": "one 360° turn in a spring or similar helix", "word": "kierros" } ] } ], "sounds": [ { "rhymes": "-uːʃən" } ], "wikipedia": [ "convolution" ], "word": "convolution" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms borrowed from Latin", "English terms derived from Latin", "English terms suffixed with -ion", "English uncountable nouns", "Entries with translation boxes", "Pages with 2 entries", "Pages with entries", "Requests for review of Scottish Gaelic translations", "Rhymes:English/uːʃən", "Rhymes:English/uːʃən/4 syllables", "Terms with Bulgarian translations", "Terms with Catalan translations", "Terms with Central Kurdish translations", "Terms with Czech translations", "Terms with Finnish translations", "Terms with French translations", "Terms with Hungarian translations", "Terms with Icelandic translations", "Terms with Italian translations", "Terms with Mandarin translations", "Terms with Polish translations", "Terms with Scottish Gaelic translations" ], "derived": [ { "word": "autoconvolution" }, { "word": "convolutional" }, { "word": "convolutionless" }, { "word": "convolution theorem" }, { "word": "convolution transform" }, { "word": "deconvolution" }, { "word": "reconvolution" }, { "word": "Titchmarsh convolution theorem" } ], "etymology_templates": [ { "args": { "1": "en", "2": "la", "3": "convolutus", "4": "", "5": "to roll together" }, "expansion": "Latin convolutus (“to roll together”)", "name": "bor" }, { "args": { "1": "en", "2": "convolute", "3": "ion" }, "expansion": "convolute + -ion", "name": "suffix" } ], "etymology_text": "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.", "forms": [ { "form": "convolutions", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "~" }, "expansion": "convolution (countable and uncountable, plural convolutions)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "convolve" }, { "word": "convolute" }, { "word": "convoluted" }, { "word": "autocorrelation" }, { "word": "cross-correlation" } ], "senses": [ { "glosses": [ "A twist or fold." ], "links": [ [ "twist", "twist" ], [ "fold", "fold" ] ], "tags": [ "countable", "uncountable" ] }, { "glosses": [ "Any of the folds on the surface of the brain." ], "links": [ [ "fold", "fold" ], [ "surface", "surface" ], [ "brain", "brain" ] ], "tags": [ "countable", "uncountable" ] }, { "glosses": [ "The shape of something rotating; a vortex." ], "links": [ [ "rotating", "rotating" ], [ "vortex", "vortex" ] ], "tags": [ "countable", "uncountable" ] }, { "glosses": [ "The state or condition of being convoluted." ], "links": [ [ "convoluted", "convoluted" ] ], "tags": [ "countable", "uncountable" ] }, { "categories": [ "English terms with quotations", "en:Functional analysis", "en:Mathematics" ], "examples": [ { "text": "1934, Aurel Wintner,\nThe 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." }, { "ref": "1997, Richard Tolimieri, Myoung An, Chao Lu, Algorithms for Discrete Fourier Transform and Convolution, 2nd edition, Springer, page 101:", "text": "Linear convolution is one of the most frequent computations carried out in digital signal processing (DSP).", "type": "quote" }, { "ref": "1994, Semen B. Yakubovich, Yurii F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Springer, page 183:", "text": "In Chapter 11 we considered H-convolutions of generalized H-transforms. 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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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