% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----
clc; close all; clear; 

x       = linspace( -3, +3, 100 ); 
y       = zeros(1,length(x)); 
inds    = find(x>0 & x<1);
y(inds) = 1; 

% the original step function: 
% 
plot( x, y, '-' ); axis( [-3, +3, -0.5, 1.5] ); title('initial step function');
saveas( gcf, '../../WriteUp/Graphics/Chapter6/chap_6_prob_27_initial_step.eps', 'psc2' );

% the flipped step function: 
% 
plot( x, fliplr(y), '-' ); axis( [-3, +3, -0.5, 1.5] ); title('flipped step function');
saveas( gcf, '../../WriteUp/Graphics/Chapter6/chap_6_prob_27_flipped_step.eps', 'psc2' );

% the flipped step shifted by a=1/2 to the right:
%
a  = 3/4;
yF = fliplr(y); 
xS = x+a; % shift x by a 
plot( xS, yF, '-' ); axis( [-3, +3, -0.5, 1.5] ); title(['flipped step function shifted right by ',num2str(a)]);
saveas( gcf, '../../WriteUp/Graphics/Chapter6/chap_6_prob_27_flipped_shifted.eps', 'psc2' );

% plot the fixed exponential function on top of this: 
% 
lambda   = 2; 
yE       = lambda * exp( -lambda * xS ); 
inds     = find( xS<0 ); 
yE(inds) = 0; 
plot( xS, yF, 'b-' ); hold on; 
plot( xS, yE, 'r-' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter6/chap_6_prob_27_flipped_shifted_w_exp.eps', 'psc2' );