The GATE Grind

GATE 2017 EE – Question 17

Signals and Systems · Linear time invariant and causal systems · 1 mark · Multiple choice

Consider the system with following input-output relation

$$y[n] = (1 + (-1)^n)\,x[n]$$

where $x[n]$ is the input and $y[n]$ is the output. The system is

  1. invertible and time invariant
  2. invertible and time varying
  3. non-invertible and time invariant
  4. non-invertible and time varying

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Show answer and explanation

Correct answer: (D) non-invertible and time varying

Explanation

For odd $n$ the factor $1 + (-1)^n$ is 0, so the output is 0 whatever the input is, and the system cannot be inverted. Shifting the input by one sample changes which samples get zeroed, so the system is also time varying.