Iterative nonparametric spectrum estimation

Starting with the traditional spectrum estimation technique, a new iterative nonparametric algorithm is developed. In each iteration of the algorithm, the effect of the previous spectral estimate is removed from the original signal by inverse filtering by a minimum-phase impulse response to obtain a residual signal whose spectral characteristics are then estimated to improve the previous estimate. The algorithm in each iteration decreases the bias of the resulting spectral estimate, without increasing its final variance. Identification of the corresponding system minimum-phase finite duration impulse response is inherent in the proposed procedure. The whole procedure can be carried out with the numerical stability of FFT's, without solving any kind of equations. This algorithm is not suitable for very narrowband spectral shapes estimation from small amounts of data. Properties of the proposed estimator are derived in detail. Experimental results show that the algorithm converges in a small number of iterations, and demonstrate that the algorithm provides very accurate spectral estimates compared with parametric methods based on ARMA models.