Question

For the exponential random variable with p(x) = e^(−x) for 10> x ≥ 0, obtain the 4-level uniform quantizer using MATLAB. You have to vary the step size (delta) in order to find the optimum step size that would minimize the distortion D. ( formula of distortion is found on the graph ). Note, b1 = delta, b2 = 2*delta, b3 = 3*delta, b4 = 10 and Y1 = 0.5* delta, Y2 = 1.5*delta, Y3 = 2.5*delta, Y4 = 3.5* delta.

gi D- 2 bnsio 2

Answer 1

MATLAB Code:

close all
clear
clc

delta = 0.001:0.001:5;
D_List = zeros(1, length(delta));
parfor d = 1:length(delta)
b = [delta(d)*(0:3) 10];
y = delta(d)*(0.5:1:3.5);
D = 0;
for i = 1:4
D = D + integral(@(x) ((x - y(i)).^2) .* exp(-x), b(i), b(i+1));
end
D_List(d) = D;
end

plot(delta, D_List)
xlabel('\Delta'), ylabel('D')

opt_delta = delta(D_List == min(D_List));
fprintf('Optimum delta = %.4f\n', opt_delta)

Output:

Optimum delta = 1.0310

Plot:

3.5 r 2.5 1.5 0.5 0 0.5 152 2.5 3 3.5 44.5 5