AN ADAPTIVE ARMA 4-LINE LATTICE FILTER FOR SPECTRAL ESTIMATION WITH FREQUENCY-WEIGHTING

This paper proposes a method for designing an adaptive four-line lattice filter which can perform ''frequency-weighting spectral estimation.'' Frequency-weighting spectral estimation is a method by which we can obtain more accurate spectral estimation for some frequency bands than for others. By using a suitable ''frequency-weighting function,'' denoted as an ARMA model, we can obtain an estimated spectrum by arbitrarily weighting some frequency bands more heavily than others. If the frequency-weighting function has the property of a low-pass filter, we can estimate the spectrum of the reference model accurately with a reduced ARMA order in the low frequency band. Therefore, the frequency-weighting method is useful for accurately estimating models with a reduced ARMA order in the specified frequency band. Further, using the proposed algorithm, we can estimate spectra of time-varying models with an exponentially weighted sliding window, and we can also estimate the input signal of the reference model by assumption. In this paper, we introduce the order-update and the time-update recursive formulas and also the frequency-weighting method for the proposed filter. In order to verify the proposed algorithm, we present a number of experiments of spectral estimation for a time-varying and unknown-input model.