%		     The University of Queensland
%     School of Information Technology & Electrical Engineering
%	     COMS3100/7100 Introduction to Communications

% Generate graphs which demonstrate the Gibbs effect for the sinc
% function

% Define the array of radian frequencies at which we will sample
% the successive approximations to the DTFT

omega = -pi:pi/1024:pi;

% The DTFT of the sinc function is a square wave in the frequency
% domain --- we define this now

X = zeros(1, 2049);
X(513:1536) = 2;

% The graphs will be drawn in a for loop.  We define here the list
% of values for M which we use in the loop, as well as the the colour
% codes for each of the plots

Mlist = [1, 3, 7, 19];
colourlist = ['r', 'g', 'b', 'm'];

% Now for the main loop in which each of the graphs are drawn

for i = 1:4,

  % Get the value of M for this graph and generate n, the list of
  % time-domain samples

  M = Mlist(i);
  n = -M:M;

  % Generate the matrix whose elements are n omega, n increasing down
  % the columns, omega across the rows

  nomega = n' * omega;

  % To generate X_M, we need only multiply a row vector of the
  % time-domain samples of x[n] by the matrix whose rows are
  % complex exponentials (the complex exponents of the elements
  % of nomega, defined above)

  XM = sinc(n / 2) * exp(j * nomega);

  % Now follows the actual plotting commands

  subplot(2, 2, i);

  % First plot the Mth order approximation to the DTFT, X_M[e^jw]

  plot(omega / pi, real(XM), colourlist(i));
  hold on;

  % Then also plot the function X[e^jw] to which the approximations
  % converge

  plot(omega / pi, X, 'k:');
  hold off;

  % Set up labels and ensure uniform scaling on each graph

  xlabel('\fontname{times}\it\omega\rm (\times \pi)');
  ylabel(['\fontname{times}\itX\rm_{', num2str(M), '}(\ite^{j\omega}\rm)']);
  xlim([-1, 1]);
  ylim([-0.5, 2.5]);
end;