In this paper we present first experimental results with a novel audio coding technique based on approximating Hilbert envelopes of relatively long segments of audio signal in critical-band-sized sub-bands by autoregressive model. We exploit the generalized autocorrelation linear predictive technique that allows for a better control of fitting the peaks and troughs of the envelope in the sub-band. Despite introducing longer algorithmic delay, improved coding efficiency is achieved. Since the described technique does not directly model short-term spectral envelopes of the signal, it is suitable not only for coding speech but also for coding of other audio signals.