GATE EC 2026 Set 1 — Question 47
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Question
Consider the discrete time system (S) with input and output as shown in the Figure. The two sub-systems represented by their impulse responses and are linear and time invariant. Which of the following statements is necessarily TRUE?
Correct answer
(B) S is linear and time invariant.
Solution
The output summer combines the upper path and the delayed lower path (with a minus sign):
- Upper path: .
- The lower summer forms (the output is delayed by and subtracted).
- This passes through and another : .
- Output: .
- (A) Causality is not guaranteed: , are only stated to be LTI, not causal; e.g. a non-causal makes non-causal.
- (B) True: interconnections of LTI systems by addition, cascading and delays are LTI.
- (C) False: nothing in the structure is time varying.
- (D) False: every operation is linear.
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