On optimum quantization

Abstract

The problem of minimizing mean-square quantization error is considered and simple closed form approximations based on the work of Max and Roe are derived for the quantization error and entropy of signals quantized by the optimum fixed- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> quantizer. These approximations are then used to show that, when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is moderately large, it is better to use equl-interval quantizing than the optimum fixed- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> quantizer if the signal is to be subsetiuently buffered and transmitted at a fixed bit rate. Finally, the problem of optimum quantizing in the presence of buffering is examined, and the numerical results presented for Gaussian signals indicate that equllevel quantizing yields nearly optimum results.