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Linear prediction (LP) analysis, split in two stages, is proposed for a combined time-frequency analysis. The first-stage LP is used to obtain the residual signal and extract each one of its cycles, whose harmonic spectrum is then modeled by the second-stage estimate from discrete all-pole algorithms. Thus, harmonic cycle spectra are modeled with less than 1 dB in log spectral distortion (SD). Further, a method is proposed to approximate the log SD target. A linear approximation to the log power spectral ratio in the log SD gradient is shown to provide better model fit to harmonic cycle spectra.