Design of Quantizers from Histograms

The design of signal quantizers when the statistical description of the source is a histogram on a finite domain is considered. Minimum mean and minimax error criteria are discussed, both leading to the design of piecewise linear compressor functions. The problem of allocating the histogram intervals in the symmetric source density case is addressed through the use of Chebyshev probability inequalities. Finally, an adaptive implementation of the proposed system is described.