Fine quantization in signal detection and estimation

The performance lost to data quantization in signal detection and estimation procedures is considered. The performance is measured by f-divergences, which are useful indices of discrimination information between statistical hypotheses. Some properties of the f-divergences are briefly discussed, and a general result for the loss in divergence due to uniform data quantization is obtained. Several applications of this result in specific problems of signal detection and estimation being developed, and some numerical results that illustrate the asymptotic behavior of the divergence in these applications are given. The divergence lost to finite nonuniform quantization through the use of a companding model is considered, and the asymptotically optimum nonuniform quantizer within this class is derived. Some interesting problems that remain open are discussed.<
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