Spectral estimation of segmented signals with extrapolation

A method is proposed to find the power spectrum of signals with missing observations. The missing observations were first found by the linear prediction method and then an AR model was assumed and the Burg algorithm was used to estimate the spectrum for each segment of the signal. The coefficients found by Burg's method were updated every time the next value of the missing signal was predicted. After the missing observations were found then the power spectra were estimated using the following three different approaches: (a) averaging in the time domain, (b) averaging the spectra of each segment, and (c) averaging the coefficients of the AR model.