‘Instant’ Fourier transform

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‘Instant’ Fourier transform

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The fast Fourier transform andd the fast Walsh transform are too slow for some real-time applications. For binary data, an ‘instant’ Fourier transform is based on harmonic analysis in a space of 2n-tuples of 0s and 1s. Simple, modular logic finishes transforming 2n real-time serial binary data one clock pulse after the last datum arrives.

Inspec keywords: harmonic analysis; Fourier transforms

Other keywords: binary data; harmonic analysis; real time data processing applications; instant Fourier transform; modular logic

Subjects: Other numerical methods; Other numerical methods; Computational techniques

References

    1. 1)
      • E.O. Brigham . (1974) , The fast Fourier transform.
    2. 2)
      • Gibbs, J.E.: `Eine Erweiterung der harmonischen Analyse auf den dyadischen Körper als Funktionenraum', Kolloquium über die Theorie und Anwendung diskrete Signale, 1976, TH Aachen, Kurzfassungen, p. 135–138.
    3. 3)
      • Gibbs, J.E.: `Harmonic analysis in the dyadic field regarded as a function space', RSRE seminar, October 1976, p. 24.
    4. 4)
      • N.J. Fine . The generalized Walsh functions. Trans. Am. Math. Soc. , 66 - 77
    5. 5)
      • H.F. Harmuth . (1972) , Transmission of information by orthogonal functions.
    6. 6)
      • E. Hewitt , K.A. Ross . , Abstract harmonic analysis.
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