Journal article

Fundamental relations between the LMS algorithm and the DFT

The digital Fourier transform (DFT) and the adaptive least mean square (LMS) algorithm have existed for some time. This paper establishes a connection between them. The result is the "LMS spectrum analyzer," a new means for the calculation of the DFT. The method uses a set ofNperiodic complex phasors whose frequencies are equally spaced from dc to the sampling frequency. The phasors are weighted and then are summed to generate a reconstructed signal. Weights are adapted to realize a best least squares fit between this reconstructed signal and the input signal whose spectrum is to be estimated. The magnitude squares of the weights correspond to the power spectrum. For a proper choice of adaptation speed, the LMS spectrum analyzer will provide an exactN-sample DFT. New DFT outputs will be available in steady flow after the introduction of each new data sample.


    • LCAV-ARTICLE-1987-003

    Record created on 2005-04-18, modified on 2017-05-12

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