Signals and Systems I ECE 351 Computing Assignment #2

OREGON STATE UNIVERSITY
SIGNALS AND SYSTEMS I
ECE 351
COMPUTING ASSIGNMENT #2

QUESTION I
The normalized frequency is periodic with a period 2pi rads/sample.
cos ( Ω0 n )=cos ( ( Ω0 +2 πk ) n )
%% SECTION I
%part a
d=rad2deg(pi); %Angle in degrees
W0=d/3; %value in the range of [-180,180]
n=-0.5:0.01:0.5; %range of samples used in the signal analysis
k=5; %for any integer value of k=0,1,2,3...
x1=cos(W0.*n); %signal 1
x2=cos((W0+2*d*k).*n); %signal 2
%part b
figure(1)
plot(n,x1,'r');
grid on
xlabel('Samples')
ylabel('Signal x(n)')
hold on
plot(n,x2,'b');
grid on
hold off
title('Plot of Two Cosine waves: x1(n) & x2(n)');
%part c
%When the signal is obtained as a sampled continuous time sinusoid
t=-5:0.1:5;
wo=1/t; %frequency in radians/sample
T=25; %Sampling frequency
xn=cos((wo*T).*n); %sampled continuous time signal
figure(2)
plot(n,xn);
grid on
xlabel('Frequency(radians/sample)')
ylabel('Signal---x(n)')
title('Sampled Continuous Time signal')
The solution is obtained as,
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