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The effect of quantization on the performance of sampling designs

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

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

Published in:

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