Title :
Quantization error and resolution in ensemble averaged data with noise
Author :
Skartlien, Roar ; Øyehaug, Leiv
Author_Institution :
Norwegian Defence Res. Establ., Kjeller, Norway
fDate :
6/1/2005 12:00:00 AM
Abstract :
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(σ,N) of the ensemble averaged data, accounting for an ensemble of finite length N, and noise RMS σ, is obtained. Previously published results for N=1 and N→∞ are recovered. For intermediate N, we show that there is an optimal noise RMS, σopt(N), which minimizes the MSE. Such a minimum point exists regardless of the type of noise probability distribution function. Conditions on σ and N for achieving a smaller MSE than in the noise-free case (Δ2/12) are discussed. The convergence properties of MSE(σ,N) for increasing N, and the effect of applying uniformly distributed dither, is established.
Keywords :
convergence of numerical methods; mean square error methods; noise; quantisation (signal); roundoff errors; convergence property; dithering; ensemble averaged data resolution; ensemble averaging; mean square error; noise free case; optimal noise; probability distribution function; quantization error; quantizer input signal; Additive noise; Analog-digital conversion; Convergence; Helium; Noise level; Noise reduction; Probability distribution; Quantization; Signal resolution; Wideband; Dithering; ensemble averaging; optimal noise; quantization; super resolution;
Journal_Title :
Instrumentation and Measurement, IEEE Transactions on
DOI :
10.1109/TIM.2005.847116