Separable estimation of discrete and continuous spectra of signal with mixed spectrum

The authors investigate a method for estimating the mixed spectra of a signal composed of multiple sinusoids and an autoregressive (AR) process. An inverse filtering approach is taken in which they apply the high-resolution Toeplitz approximation method to the filtered signal to estimate the frequencies of the sinusoids. The optimum inverse filter is adjusted in a data-adaptive way, using only received signals, so as to minimize a specified criterion. Thus the coefficients of the inverse filter give the estimate of the AR parameter. Two kinds of criterion are proposed. The first one utilizes the received signal itself. The other one consists of the differences between the autocorrelation function of the filtered signal and that of the reconstructed sinusoids with the estimated frequencies and amplitudes. The number of sinusoids and the order of the AR part are estimated on the basis of the minimum of the criterion. The authors show that even when the additive noise is white, the inverse filtering approach can improve the resolution of the frequency estimate by compensating the errors in the calculated autocorrelation function