Question

An LTI system having transfer function s^2+1/s^2+2s+1 and input x(t) =sin(t+1) is in steady state.  The output is sampled at ws rad/s to obtain the final output {y (k)}. Which of the following is true?

(a) Y is zero for all sampling frequencies ws

(b) Y is non zero for all sampling frequencies ws

(c) Y is non zero for ws>2 but zero for ws<2

(d) Y is zero for ws>2 but non zero for ws<2

The question was asked in exam.

My question comes from Spectrum Analysis of Sampling Process topic in portion Digital Control Systems of Control Systems

Answer 1

The correct option is (a) Y is zero for all sampling frequencies ws

To explain I would say: x (t) =sin (t+1)

w = 1 rad/s

X(s) = e^s/s^2+1

Y(s) = e^s/s^2+2s+1

Y (∞) =0.