Consider the analog signal xat 3cos 100pi t What is the fre

Consider the analog signal x_a(t) = 3cos 100pi t What is the frequency of the analog signal. Determine the minimum sampling rate required to avoid aliasing. Suppose the signal is sampled at a rate f_s = 200 Hz, what is the discrete-time signal obtained after sampling. Suppose the signal is sampled at a rate f_s = 75 Hz what is the discrete time signal obtained after sampling. What is the frequency of the sinusoid that yicls samples identical to that in part (c).

Solution

a) Frequency of signal f=100*pi/2pi=50 Hz

so f=50 Hz

b) minimum sampling rate to avoid aliasing is fs=2*f=2*50=100Hz

fs=100 Hz sampling rate

c) when fs=200 Hz,Xa(n)=3*cos(100*pi*n/fs)

Xa(n)=3*cos(100*pi*n/200)=3*cos(pi*n/2) Discrete signal

d) if fs=75 Hz

Xa(n)=3*cos(100*pi*n/75)=3*cos(4*pi*n/3)

e) f1=f+fs=50+200 =250 Hz

so both the signals of frequency 50 Hz and 250 Hz sampled at 200 Hz gives same discrete signal