%-------------------------------------------------------------
%
%    Randall Bramley
%    Department of Computer Science
%    Indiana University, Bloomington
%    bramley somewhere at cs dot indiana dot (allegedly) edu                             
%
% Started: Mon 04 Feb 2008, 09:05 AM
% Last Modified: Mon 16 Feb 2009, 03:58 PM
%
%-------------------------------------------------------------
more on;
echo on;

%---------------------------------------------------------------------
% 
% Example of using relational and logical operators to create arrays
% that represent signals with discontinuities, or with other values
% replacing a segment of the original signal. In Matlab, a "signal"
% is an array, and some apps require complex numbers in the array. 
% 
% Main idea: Multiply the values in an array you want to keep by ones,
% and multiply all the other values by zeros. Then you can replace
% the zero-ed out entries with other values by adding into them
% signals which themselves have zeros on the segments you want to keep.
% 
% Confusing explanation? Good. Look at the actual values, maybe
% after setting n to something smaller.
% 
% A new ingredient here is the setdiff() function. See how it is  
% used below to see how it works. 
% 
% Another new thing (to you) is how to eliminate part(s) of a vector. 
% 
%---------------------------------------------------------------------


n = 100;

x = linspace(1,10,n);

y = sin(x);
figure;
plot(x, y,  'b+-');
title('Unmodified sine function');
xlabel('Radians');
ylabel('signal = f(x)');

z1 = (y >= 0).*y;       % Gives array same as y, but with negatives values
                        % set to zero.
figure;
plot(x, z1,  'g*-');
title('Sine with negative values replaced by zeros');
xlabel('Radians');
ylabel('signal = f(x)');


z2 = z1 + 0.5*(y < 0);   % Where sin(x) is negative, add 1/2
figure;
plot(x, z2,  'r*-');
title('Sine with negative values having 1/2 added');
xlabel('Radians');
ylabel('signal = f(x)');

z3 = (x <= 8) .* z2;     % Set values past x = 8 to be zero
figure;
plot(x, z3,  'mo-');
title('Sine with values of x over 8 set to zero');
xlabel('Radians');
ylabel('signal = f(x)');

I     = find(x <= 8);
J     = setdiff(1:n, I);
z4    = (x <= 8) .* z2;  
z4(J) = NaN;
figure;
plot(x, z4,  'kp-');
title('Sine with values of x over 8 replaced with NaN');
xlabel('Radians');
ylabel('signal = f(x)');

echo off;
disp('Compare figures 4 and 5 to see why NaN can be useful.');
disp('What if +/- infinity is used instead of NaN?')
disp('-------------------------------------------------------');


disp('Next, compare using NaN and deleting the values.')
disp('Spot the difference? What does it imply about NaNs and plots?');
z5    = (x <= 8) .* z2;  
z5(J) = [];
x(J)  = [];
figure;
plot(x, z5,  'mv-');
title('Sine with values of x over 8 deleted');
xlabel('Radians');
ylabel('signal = f(x)');

unstack
more off;