Choice of Quantization Interval for Finite-Energy Fields

We consider in this paper how to encode a finite-energy random field via a finite number of bits. We present a method giving rise to a finite-bit representation for a given field. We analyze the overall reconstruction error associated with this method, and see that it is a summation which consists of the error coming from the sampling and quantization domains. Then, we search for the best sampling and quantization parameters to get the optimal reconstruction error for a given number of bits. This optimization leads to the number of bits versus reconstruction error curve consisting of best achievable points, which is reminiscent of rate distortion curve in information theory.