Question

Consider an analog signal x(t) = 2 cos(2π600t). The signal is sampled at a rate 3000 samples per second and 20 samples are saved to memory. Sketch the magnitude of the length 20 DFT of the sampled data. For credit, clearly label axes, and exactly sketch the magnitudes (if you connect points in a line drawing, rather than a “stem” plot, then clearly mark the points themselves).

Answer 1

%plot analog signal
T=1/600
t=0:T/100:4*T
x=2*cos(2*pi*600*t)
subplot(221)
plot(t,x,'b')
xlabel('t')
ylabel('x(t)')
title('Analog signal x(t)')

%plot sampled signal

N=20
n=0:1:N-1
fs=3000
Ts=1/fs
t=n*Ts
x=2*cos(2*pi*600*t)
subplot(222)
stem(n,x,'r')
xlabel('n')
ylabel('x(n)')

%20 point DFT of sampled signal
Xk=fft(x,N)
k=0:1:N-1
subplot(2,2,[3,4])
plot(k,abs(Xk),'o-')
xlabel('k')
ylabel('X(k)')
title('Magnitude response')

Analog signal x(t) 2 2 G -2 2 0 0.0010.0020.0030.0040.0050.0060.007 0 10 15 20 Magnitude response 20 15 10 15 20