Quantization for signal detection and representation

For digital representation of analog data the minimum mean-squared-error criterion is commonly used as a criterion for the basis of optimum quantizer design. In this paper we show that in some situations measures other than the minimum mean-squared-error may be more appropriate. For the signal representation problem, it is shown that the mean-absolute-error criterion has theoretical justification, as again for some signal detection problems it is shown that the mean-squared-error criterion is not the most appropriate criterion.