A signal x (t) = 100 cos (2π × 103) t is ideally sample

Home » Communication » Communication miscellaneous » Question

A signal x (t) = 100 cos (2π × 10³) t is ideally sample with sampling period of 50 μ sec and then passed through an ideal low-pass filter with cut-off frequency of 15 kHz.
Which of the following frequencies is/are present at the filter output?

1. 12 kHz only
2. 8 kHz only
3. 12 kHz and 9 kHz
4. 12 kHz and 8 kHz

Correct Option: D

Given x(t) = 100 cos (24π × 10³t)
Hence f_m = 12 kHz

f_s =	1	=	1
	T		50 × 10⁻⁶

=	1000 × 10³	= 20 kHz
	50

given that the cut-off frequency of a LPF is 15 kHz. Therefore, the frequencies passed through LPF are f_m and f_s – f_m i.e., 12 kHz and 8 kHz, since given that LPF cut-off frequency 15 kHz.
Hence alternative (D) is the correct choice.