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Every time I've read "first Fourier transform", I've assumed it to be a misspelling of the fast Fourier transform. Recently though, I saw the term in both the title and keywords of an article from a seemingly serious, albeit not peer-reviewed, journal, Japanese Circulation Journal.

Development of a new analytical method for the electrocardiogram using short-time first Fourier transforms doesn't cite any resource or explain the algorithm. (fulltext PDF)

Is there a "first" Fourier transform?

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    $\begingroup$ The article refers to fast Fourier transforms in the text (see Figure 3, for instance). So I assume this too is a mistake. Brings back fond memories of my first Fourier transform, written in Basic, and not fast. $\endgroup$ – mtrw Dec 19 '11 at 13:58
  • $\begingroup$ @mtrw: That figure text is the only mention of the fast FT (except for one reference), while the "first" FT is mentioned twice. $\endgroup$ – user42 Dec 19 '11 at 14:01
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Independently of what they call it, the process described in the paper is precisely the Fast Fourier Transform. This is made obvious by the FFT algorithm they describe, including the Gold-Rader bit-reversal procedure.

On a side note, if one tries Googling "SFFT", the S in the acronym stands for anything from sliding to spherical, but the F's always stand for Fast Fourier.

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