A method for rapidly estimating power spectral density components .rho.(f) in the spectrum of an input signal, by first digitizing the input signal over a selected time interval at a selected sample rate; computing an m-th order prediction error energy as an arithmetic mean of forward and backward prediction error energies; and then computing an m-th order prediction error power from a previous reflection coefficient .GAMMA. computation. A control parameter .alpha. is generated; using .alpha. and .GAMMA., an m-th order entropy H and free energy F are then computed, from which is computed m-th order reflection coefficients as extremes of the m-th order Free energy. If the proper extremes are not found, new feedback for the (m+1)-st order solution is generated. If the proper extremes are found, the spectral components are computed and recorded.