This paper aims at estimating the fundamental frequency (pitch) and the vocal tract resonant frequencies (formants) from new-born infant cry signals. Such parameters are of interest in exploring brain function at early stages of child development, for the timely diagnosis of neonatal disease and malformation. The paper compares a spectral parametric technique and the cepstrum approach, extending previous results. The parametric technique is based on autoregressive models whose order is adaptively estimated on subsequent signal frames by means of a new method. This allows the correct tracking of pitch and formant variations with time. The traditional cepstrum approach is modified in order to follow signal variability. In particular, the cepstrum spectral resolution is improved by applying the chirp Z-transform (CZT) and by adaptively varying the `lifter' length. The two methods are tested on simulated data, as far as robustness to noise and spectral resolution are concerned, and are then applied to real baby cry data.