The effect of quantization on the performance of sampling designs

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...

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Bibliographic Details
Published in:IEEE transactions on information theory 1998-09, Vol.44 (5), p.1981-1992
Main Authors: Benhenni, K., Cambanis, S.
Format: Article
Language:English
Subjects:
Convergence
Digital systems
Gaussian processes
Information theory
Integral equations
Mathematics
Quantization
Sampling
Sampling methods
Signal processing
Signal sampling
Statistics
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Summary: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/sup -2/ to n/sup -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/sup -2k-2/ to n/sup -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.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.705578