51. Monotonicity of Step Sizes of MSE-Optimal Symmetric Uniform Scalar Quantizers.
- Author
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Na, Sangsin and Neuhoff, David L.
- Subjects
- *
GAUSSIAN distribution , *LAPLACIAN matrices , *RAYLEIGH model , *PROBABILITY density function , *GAMMA functions - Abstract
For generalized gamma probability densities, this paper studies the monotonicity of step sizes of optimal symmetric uniform scalar quantizers with respect to mean squared-error distortion. The principal results are that for the special cases of Gaussian, Laplacian, two-sided Rayleigh, and gamma densities, optimal step size monotonically decreases when the number of levels $N$ increases by two, and that for any generalized gamma density and all sufficiently large $N$ , optimal step size again decreases when $N$ increases by two. Also, it is shown that for a Laplacian density and sufficiently large $N$ , optimal step size decreases when $N$ increases by just one. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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