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An Improved Inverse Filtering Method for Parametric Spectral Estimation

For a wide-sense stationary process x(k), it is well-known [1] that its power spectral spectrum Pxx(f) can be estimated by whitening the data with the inverse filter, V(z)=1/H(z), of the assumed minimum-phase rational model H(z) associated with x(k). However, the initial conditions for computing the output e(k) of the recursive filter V(z) are unknown and must be preassigned. In this paper, we propose an improved inverse filtering method which simultaneously estimates the coefficients of V(z) as well as the initial conditions. By simulation, the resultant power spectral estimator with the initial conditions being estimated is demonstrated to have much smaller variance as well as much smaller bias than that with the initial conditions wrongly set to be zero as the time constant of V(z) is comparable to the number of data.