Monotonicity of Step Sizes of MSE-Optimal Symmetric Uniform Scalar Quantizers

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.