Question

Is the system time invariant: y(t) = x(4t)?

(a) YES

(b) NO

I have been asked this question in a dream while sleeping

This interesting question is from Properties of Systems topic in division Signals and Systems Basics of Signals and Systems

Answer 1

The correct answer is (b) NO

The best explanation: A system is said to be time invariant if a change input causes the same change in output.

For change in input by T

⇒ y(t, T) = x(4(t – T)) = x(4t – 4T)  Equation 1

For the same change in output

⇒ y(t – T) = x(4t – T)    Equation 2

Equation 1 is not equal to equation 2.

∴ The system is not time invariant or is time variant.