The GATE Grind

GATE 2026 EC – Question 47

Networks, Signals and Systems · LTI Systems · 2 marks · Multiple choice

Consider the discrete time system (S) with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_1[n]$ and $h_2[n]$ are linear and time invariant. Which of the following statements is necessarily TRUE?

Diagram for GATE 2026 EC question 47
  1. S is causal.
  2. S is linear and time invariant.
  3. S is linear and time varying.
  4. S is non-linear.

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Show answer and explanation

Correct answer: (B) S is linear and time invariant.

Explanation

S is built only from LTI blocks ($h_1$, $h_2$, delays, adders and subtractors), so the interconnection is linear and time-invariant. Causality depends on $h_1$ and $h_2$, which are not specified to be causal.