Quantization error and resolution in ensemble averaged data with noise

R. Skartlien

doi:10.1109/TIM.2005.847116

2005-06-01

PRE

R. Skartlien *

Leiv Øyehaug

DOI：10.1109/TIM.2005.847116

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摘要

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We investigate the properties of ensemble averaged data from a uniform quantizer, when the quantizer input signal is noisy. An expression for the mean-square error (MSE) MSE(sigma, N) of the ensemble averaged data, accounting for an ensemble of finite length N, and noise RMS sigma, is obtained. Previously published results for N = 1 and N -> infinity are recovered. For intermediate N, we show that there is an optimal noise RMS, sigma(opt) (N), which minimizes the MSE. Such a minimum point exists regardless of the type of noise probability distribution function. Conditions on sigma and N for achieving a smaller MSE than in the noise-free case (Delta(2)/12) are discussed. The convergence properties of MSE(sigma, N) for increasing N, and the effect of applying uniformly distributed dither, is established.

Keyword:

dithering

ensemble averaging

optimal noise

quantization

super resolution