Auto-regressive modeling is applied for approximating the temporal evolution of spectral density in critical-band-sized sub-bands of a segment of speech signal. The generalized auto-correlation linear predictive technique allows for a compromise between fitting the peaks and the troughs of the Hilbert envelope of the signal in the sub-band. The cosine transform coefficients of the approximated sub-band envelopes, computed recursively from the all-pole polynomials, are used as inputs to a TRAP-based speech recognition system and are shown to improve recognition accuracy.