Question

THTCos (200Tt) -oo<t< oo. We want to convert = {0,1,2,...} Problem 1. Suppose we have a continuous-time signal r(t) (t) into a discrete-time signal yn] where we sample the signal every t= nT, seconds for n a. Determine the frequency fo of the cosine in Hertz and its corresponding period (T = 1/fo). b. Plot the continuous signal rt) for t = [0,4T] seconds so that four periods of the signal are plot command) plotted (use the (0, 1, 2, 3, 4 Now, assume that T and sample r(t) to yield y1 [n. Plot the discrete signal y1 [n] for n = samples (use the stem command c. seconds and sample r(t) to obtain y2[n]. Plot y2[n] for n = d. Now, assume that T, (use the stem command) {0,1,2,..., 16} samples at these two different sampling rates, what do you observe about Having sampled the same continuous signal e. each sampled sequence? Does anything seem problematic about either one?

Answer 1

Solution:

(a) the angular frequency
w=200
the fundamental frequency
fo w/2T 200T/2T 100H2

(b)

MATLAB code for continuous signal

%--------- Code starts here -----------%

T=1/100;
t=0:0.001:4*T
x=((1/1000).^t) .* cos(200*pi*t);
plot(t,x,'k')
grid on
title('continuous plot')
xlabel('time'),ylabel('x')

%----------------- END ------------------%

plot:

continuous plot 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 time CN - -

(c,d)

plot of discrete signal

%--------- Code starts here -----------%

% %-------- solution (c) -----------%
n1=0:1:4;
Ts=1/100;
y1=((1/1000).^(n1*Ts)) .* cos(200*pi*n1*Ts)
subplot(1,2,1)
stem(n1,y1,'*r')
axis([0 8 0 2])
title('Ts=1/100')
xlabel('n1');ylabel('y1')

%------- solution (d) --------%
n2=0:1:16;
Ts=1/400;
y2=((1/1000).^(n2*Ts)) .* cos(200*pi*n2*Ts)
subplot(1,2,2)
stem(n2,y2,'*r')
axis([0 16 0 2])
title('Ts=1/400')
xlabel('n2');ylabel('y2')

%---------------- END ------------------%

plot:

Ts 1/400 Ts 1/100 2 2 1.8 1.8 1.6 1.6 1,4 1,4 1.2 1.2 1+ 1* 0.8 0.8 0.6 0.6 0,4 0.4 0.2 0.2 0 0 0 0 2 4 10 15 n1 n2 LO 7! LA

(e) When the signal x(t) is sampled by higher frequency (1/100) the sampled signal has more information stored in it.The sampled signal with lower frequency contains only one sample in it.