On quantization and its impact on the exact recovery of high order moments

This paper addresses the problem of the exact recovery of unquantized moments from their quantized counterparts. A brief review of amplitude quantization and its impact on the Exact Moment Recovery (EMR) problem is given. In particular, a special class of order p, called L_p, for which EMR is always achieved regardless of the quantization fineness used, is introduced together with some new results on its properties. Due to the tremendous practical gains that can accrue from the use of 1-bit quantized members of L₁, it is shown how to force any signal to become a member of this class, hence naturally re-discovering the dithered quantization process. Two approaches to the EMR problem and some simulation results which are in very good agreement with the theory, are presented.