Useful Approximations to Optimum Quantization

Although the exact formulation for the optimum quantization of random signals is known, the determination of the optimum uniform or nonuniform quantizer can only be done currently by cumbersome computer techniques. In this paper approximate methods are presented which, for a given number of quantization levels, reduce the determination of the optimum quantizer to a one-dimensional problem. Expressions for the resulting distortion are obtained which allow a simple discussion of the merits of nonuniform quantization.