% EE-3220 Digital Signal Processing
% Wednesday 4 December 2013
% Dr. Durant
% Demonstrate periodicity in frequency - see page 33 of textbook for more information.
w1 = 2*pi*0.375; % radians per sample
w2 = 2*pi*1.375; % 2pi more radians per sample.
% After trying this, instead of (0.375+1) for w2, try (0.375-1). Note that this
% results in a negative frequency for the cosine. What is the relationship
% between the cos(x) and cos(-x)? What does this tell you about negative frequencies?
% Also, try other values such as 0.2 and 1.2, etc.
n = 0:4; % sample numbers
y1_5 = cos(w1*n); % sampled cosines
y2_5 = cos(w2*n);
plot(n,y1_5,'ko', n,y2_5,'bo') % Plot both sampled cosines vs sample number; blacK and Blue circles
xlabel('Sample number')
t = linspace(0,max(n)); % see what's going on between the integer samples, default 100 samples for plenty of detail (approximate continuous signal)
hold on % add to existing plot instead of replacing it
plot(t,cos(w1*t),'k-', t,cos(w2*t),'b-')
hold off
legend('y1 samples' ,'y2 samples' ,...
'y1 continuous', 'y2 continuous','Location','EastOutside')