clc; clear; clf;
% non-linear transforms 
warning off;

%the number of the input-output bits...
nbits_in = 15; 
nbits_out = 7;

% define the range
x_min = -2^nbits_in  ;
x_max = + 2^nbits_in -1;
in_range =  x_max - x_min;

step = 100;
x = x_min:step:x_max;

y_min = - 2^nbits_out  ;
y_max = + 2^nbits_out -1;
out_range =  y_max - y_min;

% 1. Compression: x input; y output
n = length(x);
for i=1:n,
    if x(i) >= 0,
        y(i) = out_range * log2(x(i) /  in_range + 1) / 2;
    else
        y(i) = -out_range * log2(x(i) / in_range - 1) / 2;
    end;
end;


% 2. Extention: y input ; xb output
for i=1:n,
    if y(i) >=0,
        xb(i) = in_range * 2^(2*y(i) / out_range) - in_range;
    else
        xb(i) = - in_range *( -1 / ( 2^(2*y(i) / out_range)) )  + in_range ;
    end;
end;



subplot(221), stairs(x,y); title('Compression'); 
axis([x_min x_max y_min y_max]); grid;

subplot(222), stairs(y,xb); title('Expanding');
grid;
% axis([x_min x_max x_min x_max]);

subplot(223), plot(x, xb);grid;
title('transfer characteristic');

subplot(224),  stairs(x, (xb -x) ./ x .* 100); 
axis([x_min x_max x_min x_max]);title('Reconstruction Error [%]');