# Fourier analysis

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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 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, 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 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.*