Spectral estimation from subbands

The results of previous work by the authors (see Conf. on Inform. Sci. and Syst., 1992) are used to prove that subband differential pulse-code modulation (DPCM) provides a coding gain over full-band DPCM for finite orders of prediction. The equivalence of linear prediction and autoregressive (AR) modeling equations are used to estimate source spectra from subbands. Subband decomposition of a source results in a whitening of the composite subband spectrum. This implies that for any stationary source, a p^th-order prediction error filter (PEF) can be found that is better than the p^th PEF obtained by solving the Yule-Walker equations resulting from full-band data. The existence of such a superoptimal PEF is demonstrated, and a method to optimally allocate a prediction order p_m to the m^th subband such that the sum of the p_m´s from m=1 to M equals p, where p is the full-band order of prediction and M is the number of subbands, is proposed