Question: Repeat Problem, substituting the uniform quantizer with the optimal nonuniform quantizer.

Problem: A Laplacian random variable is defined by the probability density function

f(x) = λe^-λ|x|
         2

where > 0 is a given constant.

a. Verify that the variance of a Laplacian random variable is equal to 2 / λ 2 .

b. Assuming λ = 1, design uniform quantizers with N = 2, 3, 4, 5, 6, 7, 8 levels for this source. As usual, take the interval of interest to be [-10σ, 10σ], where σ is the standard deviation of the source.

c. Plot the entropy of the quantized source and log2N as functions of N on the same figure.