See Fourier transform in All languages combined, or Wiktionary
Download JSON data for Fourier transform meaning in English (7.5kB)
{
"etymology_text": "Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.",
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"derived": [
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"word": "inverse Fourier transform"
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{
"alt": "CFT",
"word": "continuous Fourier transform"
},
{
"alt": "DFT",
"word": "discrete Fourier transform"
},
{
"alt": "FFT",
"word": "fast Fourier transform"
},
{
"alt": "FTIR",
"word": "Fourier-transform infrared spectroscopy"
}
],
"examples": [
{
"text": "Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.",
"type": "example"
},
{
"text": "The Fourier transform of a function of time is a complex function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency.",
"type": "example"
},
{
"ref": "2002, J. F. James, A Student's Guide to Fourier Transforms, 2nd edition, Cambridge University Press, page 116",
"text": "Since a separate integration is needed to give each point of the transformed function, the process would become extremely tedious if it were to be attempted manually and many ingenious devices have been invented for preforming Fourier transforms mechanically, electrically, acoustically and optically.",
"type": "quotation"
},
{
"text": "2005, Emmanuel Letellier, Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras, Springer, Lecture Notes in Mathematics 1859, page 1,\nThe trigonometric sums of 𝒢^F are thus (up to a scalar) the Fourier transforms of the characteristic functions of the G^F!!-orbits of 𝒢^F."
},
{
"text": "2012, David Brandwood, Fourier Transforms in Radar and Signal Processing, Artech House, 2nd Edition, page 1,\nThe Fourier transform is a valuable theoretical technique, used widely in fields such as applied mathematics, statistics, physics, and engineering."
}
],
"glosses": [
"A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion."
],
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"word": "integral transform"
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"id": "en-Fourier_transform-en-noun-L5yIgGqN",
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"qualifier": "harmonic analysis",
"raw_glosses": [
"(mathematical analysis, harmonic analysis, physics, electrical engineering) A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion."
],
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{
"tags": [
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"word": "FT"
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"translations": [
{
"code": "nl",
"lang": "Dutch",
"sense": "mathematics: a type of integral transform",
"word": "Fouriertransformatie"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "mathematics: a type of integral transform",
"word": "Fourier-transformatie"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "mathematics: a type of integral transform",
"word": "Fourier-muunnos"
},
{
"code": "fr",
"lang": "French",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "transformation de Fourier"
},
{
"code": "gl",
"lang": "Galician",
"sense": "mathematics: a type of integral transform",
"word": "transformada de Fourier"
},
{
"code": "de",
"lang": "German",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "Fouriertransformation"
},
{
"code": "de",
"lang": "German",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "Fourier-Transformation"
},
{
"code": "el",
"lang": "Greek",
"roman": "metaschimatismós Fourié",
"sense": "mathematics: a type of integral transform",
"tags": [
"masculine"
],
"word": "μετασχηματισμός Φουριέ"
},
{
"code": "it",
"lang": "Italian",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "trasformata di Fourier"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Fūrie henkan",
"sense": "mathematics: a type of integral transform",
"word": "フーリエ変換"
},
{
"code": "fa",
"lang": "Persian",
"roman": "tabdil-e furiye",
"sense": "mathematics: a type of integral transform",
"word": "تبدیل فوریه"
},
{
"code": "pl",
"lang": "Polish",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "transformacja Fouriera"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "tranformare Fourier"
},
{
"code": "ru",
"lang": "Russian",
"roman": "preobrazovánije Furʹjé",
"sense": "mathematics: a type of integral transform",
"tags": [
"neuter"
],
"word": "преобразова́ние Фурье́"
},
{
"code": "es",
"lang": "Spanish",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "transformada de Fourier"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "mathematics: a type of integral transform",
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"word": "Fouriertransform"
}
],
"wikipedia": [
"Fourier transform",
"Jean Baptiste Joseph Fourier"
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],
"word": "Fourier transform"
}
{
"derived": [
{
"word": "inverse Fourier transform"
},
{
"alt": "CFT",
"word": "continuous Fourier transform"
},
{
"alt": "DFT",
"word": "discrete Fourier transform"
},
{
"alt": "FFT",
"word": "fast Fourier transform"
},
{
"alt": "FTIR",
"word": "Fourier-transform infrared spectroscopy"
}
],
"etymology_text": "Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.",
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"text": "Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.",
"type": "example"
},
{
"text": "The Fourier transform of a function of time is a complex function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency.",
"type": "example"
},
{
"ref": "2002, J. F. James, A Student's Guide to Fourier Transforms, 2nd edition, Cambridge University Press, page 116",
"text": "Since a separate integration is needed to give each point of the transformed function, the process would become extremely tedious if it were to be attempted manually and many ingenious devices have been invented for preforming Fourier transforms mechanically, electrically, acoustically and optically.",
"type": "quotation"
},
{
"text": "2005, Emmanuel Letellier, Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras, Springer, Lecture Notes in Mathematics 1859, page 1,\nThe trigonometric sums of 𝒢^F are thus (up to a scalar) the Fourier transforms of the characteristic functions of the G^F!!-orbits of 𝒢^F."
},
{
"text": "2012, David Brandwood, Fourier Transforms in Radar and Signal Processing, Artech House, 2nd Edition, page 1,\nThe Fourier transform is a valuable theoretical technique, used widely in fields such as applied mathematics, statistics, physics, and engineering."
}
],
"glosses": [
"A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion."
],
"links": [
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"qualifier": "harmonic analysis",
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"(mathematical analysis, harmonic analysis, physics, electrical engineering) A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion."
],
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{
"code": "nl",
"lang": "Dutch",
"sense": "mathematics: a type of integral transform",
"word": "Fouriertransformatie"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "mathematics: a type of integral transform",
"word": "Fourier-transformatie"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "mathematics: a type of integral transform",
"word": "Fourier-muunnos"
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{
"code": "fr",
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"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "transformation de Fourier"
},
{
"code": "gl",
"lang": "Galician",
"sense": "mathematics: a type of integral transform",
"word": "transformada de Fourier"
},
{
"code": "de",
"lang": "German",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "Fouriertransformation"
},
{
"code": "de",
"lang": "German",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
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"word": "Fourier-Transformation"
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{
"code": "el",
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"roman": "metaschimatismós Fourié",
"sense": "mathematics: a type of integral transform",
"tags": [
"masculine"
],
"word": "μετασχηματισμός Φουριέ"
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{
"code": "it",
"lang": "Italian",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "trasformata di Fourier"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Fūrie henkan",
"sense": "mathematics: a type of integral transform",
"word": "フーリエ変換"
},
{
"code": "fa",
"lang": "Persian",
"roman": "tabdil-e furiye",
"sense": "mathematics: a type of integral transform",
"word": "تبدیل فوریه"
},
{
"code": "pl",
"lang": "Polish",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "transformacja Fouriera"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
],
"word": "tranformare Fourier"
},
{
"code": "ru",
"lang": "Russian",
"roman": "preobrazovánije Furʹjé",
"sense": "mathematics: a type of integral transform",
"tags": [
"neuter"
],
"word": "преобразова́ние Фурье́"
},
{
"code": "es",
"lang": "Spanish",
"sense": "mathematics: a type of integral transform",
"tags": [
"feminine"
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"word": "transformada de Fourier"
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"code": "sv",
"lang": "Swedish",
"sense": "mathematics: a type of integral transform",
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"word": "Fouriertransform"
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"word": "Fourier transform"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). 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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