Consistent analogs of the Fourier uncertainty relation

G. W. Forbes, M. A. Alonso

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)


    To resolve an issue that was raised in our earlier paper in this journal [69, 340-347 (2001)], a direct analog of the standard uncertainty relation is derived for the discrete Fourier transform (DFT). This inequality gives a simple lower bound for the degree of localization of the DFT of any sequence in terms of just the localization of the original sequence. It is also shown that the earlier uncertainty relations for the Fourier transform and the Fourier series can be derived from this new relation by taking appropriate limits. Because the same cannot be said of the others, this new relation is arguably the most fundamental of the three. (C) 2001 American Association of Physics Teachers.

    Original languageEnglish
    Pages (from-to)1091-1095
    Number of pages5
    JournalAmerican Journal of Physics
    Issue number10
    Publication statusPublished - Oct 2001


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