Modeling and design of multidimensional vector-quantized M-channel subband codecs

We develop a heuristic theory for modeling, analysis, optimum filter bank design and compensation of encoding vector quantization effects in multidimensional M-band FIR filter banks. Each PDF-optimized vector quantizer is represented by a scalar nonlinear gain-plus-additive uncorrelated noise model embedded into the subband structure. We compute the mean squared reconstruction error which depends on N, the number of entries in each codebook, and k the length of each codeword (that is, the average bit rate), and on the filter coefficients. This mean squared error is then minimized subject to the perfect reconstruction constraints and the total bits for the entire bank. The algorithm gives optimum filter coefficients, compensator gains, and the bit allocations. Numerical design examples for the optimum separable and nonseparable paraunitary and biorthogonal filter banks are developed in this paper. Also, theoretical results are confirmed by extensive Monte Carlo simulation