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Linear Reconstruction of Quantized and Sampled Random Signals

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1 Author(s)
Ruchkin, D.S. ; Univ. of Rochester, Rochester, N. Y.

Techniques for optimal mean-square linear reconstruction from quantized samples of a random signal and the resulting errors are discussed in this paper. The signal is assumed to be wide-sense stationary with Gaussian statistics. The shape of the sample pulse is arbitrary. It is shown that the pulse shape has no effect upon the minimum mean-square error. An optimal linear filter for reconstruction from quantized samples and the resulting error are obtained. The mean-square error that arises when the optimal filter for unquantized samples reconstructs from quantized samples is also obtained. The errors of the above-mentioned filters are then compared. It is shown that, for sufficiently high sampling rates, the filter that takes quantizing into account can achieve a significant reduction in quantizing error relative to the filter for unquantized samples. However, when a constraint of constant channel capacity is imposed, there is essentially no difference between the optimal performances of the two filters.

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Communications Systems, IRE Transactions on  (Volume:9 ,  Issue: 4 )