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.

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IEEE Transactions on Circuits and Systems, Special Issue on Adaptive Filters, 34, 7, 814-820

 Record created 2005-04-18, last modified 2018-03-17

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