Question

The signal $x\left(t\right)=sin\left(14000\pi t\right)$, where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low-pass filter with frequency response H(f) as follows :

$H\left(f\right)=\{\begin{array}{cc}1,& \mid f\mid \le 12kHz\\ 0,& \mid f\mid >12kHz\end{array}$

What is the number of sinusoids in the output and their frequencies in kHz?

• A. Number = 2, frequencies = 7, 11
• B. Number = 1, frequency = 7
• C. Number = 2, frequencies = 2, 7
• D. Number = 3, frequencies = 2 , 7, 11

Answer 1

The correct option is D Number = 3, frequencies = 2 , 7, 11

$x\left(t\right)=sin\left(14000\pi t\right);f_m=7kHz$
$f_s=\text{9000 samples per second}$
$=9kHz$
The spectrum of the sampled signal can be given as shown below:

So, three sinusoids will be there at the output of the LPF and the frequencies of those sinusoids are 2 kHz, 7 kHz and 11 kHz.