Question

A signal represented by x(t) =5cos 400πt is sampled at a rate 300 samples/sec. The resulting samples are passed through an ideal low pass filter of cut-off frequency 150 Hz. Which of the following will be contained in the output of the LPF?

(a) 100 Hz

(b) 100 Hz, 150 Hz

(c) 50 Hz, 100 Hz

(d) 50 Hz, 100 Hz, 150 Hz

This question was posed to me in an internship interview.

The question is from Spectrum Analysis of Sampling Process topic in portion Digital Control Systems of Control Systems

Answer 1

The correct choice is (a) 100 Hz

For explanation: x (t) =5cos400πt

fm =200 Hz

The output of the LPF will contain frequencies which are less than fc =150 Hz.

So, fs-fm =300-200 =100 Hz is the only component present in the output of LPF.