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The effect of quantization on the performance of sampling designs

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2 Author(s)
Benhenni, K. ; LABSAD, Univ. Pierre Mendes France, Grenoble, France ; Cambanis, S.

The most common form of quantization is rounding-off, which occurs in all digital systems. A general quantizer approximates an observed value by the nearest among a finite number of representative values. In estimating weighted integrals of a time series with no quadratic mean derivatives, by means of samples at discrete times, it is known that the rate of convergence of the mean-square error is reduced from n-2 to n-1.5 when the samples are quantized. For smoother time series, with k=1, 2, ... quadratic mean derivatives, it is now shown that the rate of convergence is reduced from n-2k-2 to n-2 when the samples are quantized, which is a very significant reduction. The interplay between sampling and quantization is also studied, leading to (asymptotically) optimal allocation between the number of samples and the number of levels of quantization

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 5 )