Changes: Fourier analysis

Revision as of 17:30, 29 November 2010

Fourier analysis 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 analysis at the Griffith Observatory, when Tom Paris told her that her "curves don't look so great," in relation to the analysis. (VOY: "Future's End")

Data noted 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 aliens known as the Hierarchy, 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")

Fourier analysis is named after Joseph Fourier's introduction of the Fourier series.

External link

Fourier analysis at Wikipedia

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-'''Fourier analysis''', named after Joseph Fourier's introduction of the Fourier series, is the decomposition of a function in terms of a sum of sinusoidal basis functions (vs. their [[Frequency|frequencies]]) that can be recombined to obtain the original function. That process of recombining the sinusoidal basis functions is also called Fourier synthesis (in which case Fourier analysis refers specifically to the decomposition process).
+'''Fourier analysis''' was the decomposition of a periodic signal in terms of a sum of sinusoidal basis functions (versus their [[frequency|frequencies]]).
+In [[1996]], [[Rain Robinson]] performed a Fourier analysis at the [[Griffith Observatory]], when [[Tom Paris]] told her that her "''curves don't look so great,''" in relation to the analysis. ({{VOY|Future's End}})
-In late [[2377]] [[the Doctor]] played the [[The Blue Danube|Blue Danube]] [[European classical music|waltz]] in one of his recitals. When he and [[Captain]] [[Kathryn Janeway|Janeway]] were abducted by [[Alien|aliens]] known as the [[Hierarchy species|Hierarchy]], the doctor altered a recording of the waltz so that it would [[Sonics|sound]] out of tune. By perfoming 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]]")
+[[Data]] noted that he knew that [[Juliana Soong|his mother]] was an [[android]] because, as he stated, "''the intervals between blinks were governed by the Fourier system, the same mathematical formula [[Noonian Soong|my father]] used to give my blinking pattern the appearance of randomness.''" ({{TNG|Inheritance}})
-==References==
-* {{TNG|Inheritance}}
-* {{VOY|Future's End}}
+In [[2378]], [[The Doctor]] played ''[[The Blue Danube]]'' [[European classical music|waltz]] in one of his recitals. When he and [[Captain]] [[Kathryn Janeway|Janeway]] were abducted by [[alien]]s known as the [[Hierarchy species|Hierarchy]], 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}})
-==External Links==
+{{bginfo|Fourier analysis is named after {{w|Joseph Fourier}}'s introduction of the {{w|Fourier series}}.}}
-*{{wikipedia|Fourier analysis}}
+== External link ==
+* {{wikipedia}}
+[[Category:Mathematics]]