Some properties of uniform step size quantizers (Corresp.)
James Antonio Bucklew, Neal C. Gallagher · IEEE Transactions on Information Theory · 1980
Some properties of the optimal mean-square error uniform quantizer are treated. It is shown that the mean-square error (mse) is given by the input variance minus the output variance. Furthermore\lim_{N \rightarrow \infty}mse/(\Delta^{2}/12) \geq 1, whereNis the number of output levels and\Delta(a function ofM) is the step size of the uniform quantizer, with equality when the support of the random variable is contained in a finite interval. A class of probability densities is given for which the above limit is greater than one. It is shown that\lim_{N \rightarrow \infty}N^{2} \cdotmse=(b-a)^{2}/12, where(b-a)is the measure of the smallest interval that contains the support of the input random variable.