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Fourier transform


from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. a transform, applied to a function, used to determine the function's frequency composition (temporal, spatial or otherwise); it has many scientific and industrial applications, especially in signal processing.


from Wiktionary, Creative Commons Attribution/Share-Alike License

from Jean Baptiste Joseph Fourier, its inventor


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  • "Of course, if a piano and a violin play the same high C at the exact same volume, there is still some quality that feels different between the two notes. It turns out that pure tones do not occur naturally, and when a piano or violin produces a high C, the sound wave is made up of a specific combination of different pure tones. The different amplitudes and frequencies have nice relationships with one another, which is why you hear a specific note rather than a mess of clashing noises, but the single pitch you hear does not correspond to a single frequency. The hard-to-define quality of sound that allows you to identify what instrument you’re listening to is determined by the exact combination of pure tones. When different instruments all play at the same time, the various pure tones add together to create the music you hear.

    "So what do pure tones have to do with the groove on a record being able to tell David Bowie and Nina Simone apart? It turns out that any curve can be written in exactly one way as a combination of curves with uniform amplitude and frequency. In other words, the single squiggle captured in the groove of a record player can be written as a combination of pure tones. And there is only one combination that will produce any particular squiggle. The tool that makes this possible comes from mathematics and is called the Fourier transform. Combined with the fact that the sound we experience is determined by the exact combination of pure tones, this bit of mathematics explains how the vinyl record groove can completely determine the music you hear."

    -- "Which Sounds Better, Analog or Digital Music?" by Katrina Morgan (

    October 11, 2017