% EE-3220 Digital Signal Processing

% Wednesday 4 December 2013

% Dr. Durant <durant@msoe.edu>



%  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')