function [x,y,n]=bs_generate_XY(N, example)
% function [x,y,n]=bs_generate_XY(N, example )
%    Generate to random variables with a non-zero linear relationship
%    Y = a*X + N
%    INPUTS:
%      N  is the length of the generated vectors
%      example: there are 5 different examples
%               from class. 
%
%    EXAMPLE: 
%      generate y using a Gaussian PDF for x and
%      a tringular PDF for n. Also enforce a signal
%      to noise of 2.
%      example_number=1;
%      N=1000;
%      [x,y,n]=bs_generate_XY(N, example_number)
%
% EAS-8803 - edl@gatech.edu


if example ==1
	x = bs_rand('norm', [0, 2 ], N, 1);
	n = bs_rand('norm', [0, 1 ], N, 1);
	n=n-mean(n);
    a=0.8;
	y  = a*x;
	sn=2;
    n = n/std(n) * sqrt( var(y) / sn);
    y = a*x + n;
    disp(' ');
    disp( '- Generating X and Y with the following relationships:');
    disp(['         y = 0.8*x + n ']);
    disp(['         PDF(X) = Gaussian            (mean=0; var=2    )']);
    disp(['         PDF(N) = Gaussian            (mean=0;          )']);
    disp(['         Singal to noise ration SN=2  (SN=var(y)/var(n) )']);
    disp(' ');
end

if example ==2
	x = bs_rand('norm', [0, 2 ], N, 1);
	n = bs_rand('tri', [-0.4, 0, 6], N, 1);
	n=n-mean(n);
    a=0.8;
	y  = a*x;
	sn=2;
    n = n/std(n) * sqrt( var(y) / sn);
    y = a*x + n;
    disp(' ');
    disp( '- Generating X and Y with the following relationships:');
    disp(['         y = 0.8*x + n ']);
    disp(['         PDF(X) = Gaussian            (mean=0; var=2    )']);
    disp(['         PDF(N) = Triangular          (a=-0.4; b=6; c=0;)']);
    disp(['         Singal to noise ration SN=2  (SN=var(y)/var(n) )']);
    disp(' ');
end

if example ==3
	x = bs_rand('uniform', [0  18], N, 1);
    n = bs_rand('norm', [0, 15 ], N, 1);
	%n=n-mean(n);
    y = exp(x/2);	
	sn=10;
    n = n/std(n) * sqrt( var(y) / sn);
    y = exp(x/2) + n;
    disp(' ');
    disp( '- Generating X and Y with the following relationships:');
    disp(['         y = exp(x/2) + n ']);
    disp(['         PDF(X) = Uniform              (a=0; b=18        )']);
    disp(['         PDF(N) = Gaussian             (mean=0; var=15   )']);
    disp(['         Singal to noise ration SN=10  (SN=var(y)/var(n) )']);
    disp(' ');
end


if example ==4
	x = bs_rand('norm', [2, 2 ], N, 1);
	n = bs_rand('lognormal', [], N, 1 );
	%n=n-mean(n);
    a=0.8;
	y  = a*x;
	sn=2;
    n = n/std(n) * sqrt( var(y) / sn);
    y = a*x + n;
    disp(' ');
    disp( '- Generating X and Y with the following relationships:');
    disp(['         y = 0.8*x + n ']);
    disp(['         PDF(X) = Gaussian            (mean=2; var=2    )']);
    disp(['         PDF(N) = Lognormal           (mean=0;          )']);
    disp(['         Singal to noise ration SN=2  (SN=var(y)/var(n) )']);
    disp(' ');
end



return