Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications
Statistical results for system identification based on quantized observations
Automatica (Journal of IFAC)
A theory of nonsubtractive dither
IEEE Transactions on Signal Processing
Distributed Average Consensus With Dithered Quantization
IEEE Transactions on Signal Processing - Part I
Sequential signal encoding from noisy measurements using quantizers with dynamic bias control
IEEE Transactions on Information Theory
Signal Parameter Estimation Using 1-Bit Dithered Quantization
IEEE Transactions on Information Theory
Multivariate Signal Parameter Estimation Under Dependent Noise From 1-Bit Dithered Quantized Data
IEEE Transactions on Information Theory
Hi-index | 22.14 |
The Quantization Theorem I (QT I) implies that the likelihood function can be reconstructed from quantized sensor observations, given that appropriate dithering noise is added before quantization. We present constructive algorithms to generate such dithering noise. The application to maximum likelihood estimation (mle) is studied in particular. In short, dithering has the same role for amplitude quantization as an anti-alias filter has for sampling, in that it enables perfect reconstruction of the dithered but unquantized signal's likelihood function. Without dithering, the likelihood function suffers from a kind of aliasing expressed as a counterpart to Poisson's summation formula which makes the exact mle intractable to compute. With dithering, it is demonstrated that standard mle algorithms can be re-used on a smoothed likelihood function of the original signal, and statistically efficiency is obtained. The implication of dithering to the Cramer-Rao Lower Bound (CRLB) is studied, and illustrative examples are provided.