A filter for on-line estimation of spectral content

A robust filter algorithm to extract, a posteriori, the rational signal model from a noisy measurement, with little a priori information, is proposed. The spectrum and the statistics of the signal and of the corrupting noise are assumed unknown, except that the signal is assumed to have a rational spectrum. An algorithm based on system and signal theory is derived to select a set of frequencies where the signal-to-noise ratio (SNR) is high from a given measurement spectrum. The density of selected frequencies weights the importance of the measurement as a function of frequency, An estimate of the signal model is obtained from the best weighted least-squares fit to the measurement spectrum at the selected frequencies. The proposed filter has applications to control and signal processing, and a wide variety of applications are presented. Applications include: system identification of a dc motor and a two-link manipulator, extraction of a myo-electric signal from a noisy measurement, the assignment of a rational model to a vegetation tissue's impedance, and to the number density profile of atmospheric oxygen.