Multidimensional spherical coordinates quantization

Several investigators have considered polar coordinates quantization of a circularly symmetric source; in particular, the independent bivariate Gaussian source. Their schemes quantize the polar coordinates independently in an attempt to reduce the mean-square error below that of an analogous rectangular coordinates quantizer yet retain an implementation simpler than that of the optimal bivariate quantizer. The design of a spherical coordinates quantizer in dimensions with matches published results) is considered. Examples are presented along with comparisons to the rectangular (one-dimensional) and optimal schemes.