A continuous signal xt cos14 pi t is sampled at the samplin

A continuous signal x(t) = cos(14 pi t) is sampled at the sampling frequency of f_s = 10 Hz in order to obtain the discrete sequence x[n]. Would there be an aliasing problem? If x[n] is converted back to an analog signal, then what would be the frequency of the analog signal. Repeat (a) and (b) if sampling frequency of f_s = 20 Hz is used.

Solution

a)

frequency of the given signal=2*pi*f=14*pi

f=7Hz

if Fs=10Hz means its not satisfies the Nyquist citeria Fs>=2f

so it will produce Aliasing problem

b) the recived signal willhave two components 10+7hz and 10-7hz

and its filtered by Low pass signal, so the reicived signal frequency is 3HZ

c)if we choose FS=20Hz which satisfies the Nyquirst criteria.

Fs>=F.so alaiasing problem will not occur.

20+7,20-7

so the recived signal willhave 13Hz as frequency