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The sampling, quantization, and estimation of a bounded dynamic-rangebandlimited signal affected by additive independent Gaussian noise is studiedin this work. For bandlimited signals, the distortion due to additiveindependent Gaussian noise can be reduced by oversampling (statisticaldiversity). The pointwise expected mean-squared error is used as a distortionmetric for signal estimate in this work. Two extreme scenarios of quantizerprecision are considered: (i) infinite precision (real scalars); and (ii)one-bit quantization (sign information). If $N$ is the oversampling ratio withrespect to the Nyquist rate, then the optimal law for distortion is $O(1/N)$.We show that a distortion of $O(1/N)$ can be achieved irrespective of thequantizer precision by considering the above-mentioned two extreme scenarios ofquantization. Thus, a quantization precision indifference principle isdiscovered, where the reconstruction distortion law, up to a proportionalityconstant, is unaffected by quantizer's accuracy.

Estimation of Bandlimited Signals in Additive Gaussian Noise: a "Precision Indifference" Principle