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Some properties of uniform step size quantizers (Corresp.)

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2 Author(s)

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 , where N is the number of output levels and \Delta (a function of M ) 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} \cdot mse =(b-a)^{2}/12 , where (b-a) is the measure of the smallest interval that contains the support of the input random variable.

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Information Theory, IEEE Transactions on  (Volume:26 ,  Issue: 5 )