Minimum mean-squared error transform coding and subband coding

Knowledge of the power spectrum of a stationary random sequence can be used for quantizing the signal efficiently and with minimum mean-squared error, A multichannel filter is used to transform the random sequence into an intermediate set of variables that are quantized using independent scalar quantizers, and then inverse-filtered, producing a quantized version of the original sequence, Equal word-length and optimal word-length quantization at high bit rates is considered, An analytical solution for the filter that minimizes the mean-squared quantization error is obtained in terms of its singular value decomposition, The performance is characterized by a set of invariants termed second-order modes, which are derived from the eigenvalue decomposition of the matrix-valued power spectrum, A more general rank-reduced model is used for decreasing distortion by introducing bias, The results are specialized to the case when the vector-valued time series is obtained from a scalar random sequence, which gives rise to a filter bank model for quantization, The asymptotic performance of such a subband coder is derived and shown to coincide with the asymptotic bound for transform coding, Quantization employing a single scalar pre- and postfilter, traditional transform coding using a square linear transformation, and subband coding in filter banks, arise as special cases of the structure analyzed here.