Polar Quantization Revisited

A uniied analysis of several polar quantization schemes is developed by focusing on their point densities and inertial prooles and using Bennett's integral to express the mean-squared error. The subsequent analysis is straightforward and leads to new insights into the relationship between polar quantization and Cartesian quantization. With this approach, unrestricted polar quantization, which is arguably the best method, may be optimized essentially by inspection. As another example, a new polar quanti-zation method, called power law polar, is analyzed and optimized. Polar quantization with a uniform magnitude quantizer is also analyzed and optimized, using recent high-resolution results on the optimal step size and support of uniform scalar quantization for sources with unbounded support. It is shown that the optimal rate allocation gives increasingly more rate to the magnitude as total rate increases, compared to nonuniform polar, where the diierence between optimal magnitude and phase rates is asymptoti-cally a constant.