tst_conv.m

%% 
clear
clc
close all

l1 = 2.5;
l2 = 1.1;
sig = 100;

rat1 = [];
rat2 = [];
rat3 = [];
for t = 3 : 100
    num1 = l2^(2*t) + sig^2 * ((l2^(2*(t-1)) - 1)/ (l2^2 - 1));
    den1 = l1^(2*t) + sig^2 * ((l1^(2*(t-1)) - 1)/ (l1^2 - 1));
    rat1 = [rat1, num1 / den1];
    
    num2 = l2^(2*t);
    den2 = l1^(2*t);
    rat2 = [rat2, num2 * (1+sig^2) / den2];
    
    rat3 = [rat3, 1/den2];
end

% l1 = 1.5;
% l2 = 1.1;
% sig = 1;
% t = 11;
% num = l2^(2*t) + sig^2 * ((l2^(2*(t-1)) - 1)/ (l2^2 - 1));
% den = l1^(2*t) + sig^2 * ((l1^(2*(t-1)) - 1)/ (l1^2 - 1));

figure;
semilogy(rat1, 'rs')
hold
semilogy(rat2 , 'kd')
semilogy(rat3, 'bo')
legend('sigma2/sigma1', '(l1/l2)^t (1+t)', '(1/l1)^t')


%% 
% 
% clear
% clc
% close all
% rat = linspace(1.1, 100, 1000);
% 
% ours = 1 ./ log(rat);
% theirs = rat ./ (rat-1);
% 
% figure;
% plot(ours, 'rd');
% hold
% plot(theirs, 'ks');
% axis tight