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

% Plot a waveform similar to the in CCR Fig. 11.4-2

% Set up a bit stream, of which we will only plot a few

bits = [0 0 1 0 1 0 1 1 0 1 0 0 1 0 1];

% Set up a time axis (t starts at -3)

tstart = -3;
tend = length(bits) + tstart - 1;
n = tstart:tend;
t = tstart:0.1:tend;
tmat = ones(length(n), 1) * t - n' * ones(1, length(t));

% Generate the low-passed received waveform (sum of raised cosine pulse
% shapes, not covered in COMS3100/7100)

a = ((2 * bits)-1);
y = zeros(1, length(t));
for i = 1:length(bits),
    tshift = t - n(i);
    y = y + a(i) * sinc(tshift) .* cos(0.99 * pi * tshift) ...
        ./ (1 - 4 * 0.99^2 * tshift.^2);
end;

subplot(3, 1, 1);
plot(t, y);
xlim([0.4, 8.1]);
xlabel('t');
ylabel('y(t)');

% Generate the squared version

yy = y.^2;

subplot(3, 1, 2);
plot(t, yy);
xlim([0.4, 8.1]);
xlabel('t');
ylabel('y^2(t)');

% Generate a bandpass filtered version (by applying a low-pass then a
% high-pass filter)

[b, a] = butter(5, 0.22);
lp = filtfilt(b, a, yy);

[b, a] = butter(5, 0.18, 'high');
bp = filtfilt(b, a, lp);

subplot(3, 1, 3);
plot(t, bp);
xlim([0.4, 8.1]);
xlabel('t');
ylabel('cos 2 \pi r_b t');