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| + | [[File:Fourier spectral analysis.jpg|thumb|Fourier spectral analysis]] |
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| − | The '''Fourier series''' is a mathematical formula used in [[Data]]'s programming, giving his blinking the appearance of randomness. |
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| + | '''Fourier analysis''' or '''Fourier series''' was the decomposition of a periodic signal in terms of a sum of sinusoidal basis functions (versus their [[frequency|frequencies]]). |
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| + | In [[1996]], [[Rain Robinson]] performed a Fourier spectral analysis at the [[Griffith Observatory]], when [[Tom Paris]] told her that her "''curves don't look so great,''" in relation to the analysis, then suggesting she might wish to apply a [[theta band filter]]. ({{VOY|Future's End}}) |
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| − | In [[2370]], after meeting his mother, Data observed that [[Juliana Tainer]]'s blinking followed the same pattern as his own, leading him to suspect that she was an [[android]], which was later confirmed. ({{TNG|Inheritance}}) |
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| + | [[Data]] noted, in [[2370]], that he knew that [[Juliana Tainer|his mother]] was an [[android]] because, as he stated, "''the intervals between [[blink]]s were governed by the Fourier system, the same mathematical formula [[Noonien Soong|my father]] used to give my blinking pattern the appearance of randomness.''" ({{TNG|Inheritance}}) |
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| + | In [[2378]], [[The Doctor]] played ''[[The Blue Danube]]'' [[waltz]] in one of his recitals. When he and [[Captain]] [[Kathryn Janeway|Janeway]] were [[abduct]]ed by [[Zet]] and [[Nar]], The Doctor altered a recording of the waltz so that it would [[acoustics|sound]] out of tune. By performing a Fourier analysis, [[Seven of Nine]] found out that the harmonics of the piece had been modified to imitate a [[warp signature]]. The crew was able to track the signature and thereby locate The Doctor and the captain. ({{VOY|Renaissance Man}}) |
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| + | {{bginfo|Fourier analysis is named after {{w|Joseph Fourier}}'s introduction of the {{w|Fourier series}}.}} |
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== External link == |
== External link == |
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| − | * {{ |
+ | * {{wikipedia}} |
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| + | [[Category:Analyses]] |
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[[Category:Mathematics]] |
[[Category:Mathematics]] |
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Latest revision as of 19:45, 6 December 2023
Fourier spectral analysis
Fourier analysis or Fourier series was the decomposition of a periodic signal in terms of a sum of sinusoidal basis functions (versus their frequencies).
In 1996, Rain Robinson performed a Fourier spectral analysis at the Griffith Observatory, when Tom Paris told her that her "curves don't look so great," in relation to the analysis, then suggesting she might wish to apply a theta band filter. (VOY: "Future's End")
Data noted, in 2370, that he knew that his mother was an android because, as he stated, "the intervals between blinks were governed by the Fourier system, the same mathematical formula my father used to give my blinking pattern the appearance of randomness." (TNG: "Inheritance")
In 2378, The Doctor played The Blue Danube waltz in one of his recitals. When he and Captain Janeway were abducted by Zet and Nar, The Doctor altered a recording of the waltz so that it would sound out of tune. By performing a Fourier analysis, Seven of Nine found out that the harmonics of the piece had been modified to imitate a warp signature. The crew was able to track the signature and thereby locate The Doctor and the captain. (VOY: "Renaissance Man")