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GATE 2025 BM – Question 44

Signals and Systems · LTI Systems and Convolution · 2 marks · Multiple select

Systems U,V are defined by U: y(t)=x(t)²+1 and V: y(t)=x(t+1). Which are correct?

  1. U nonlinear,V linear
  2. U causal,V noncausal
  3. U noncausal,V causal
  4. Both nonlinear

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Show answer and explanation

Correct answer: (A) U nonlinear,V linear; (B) U causal,V noncausal

Explanation

U fails superposition because of both squaring and its nonzero output for zero input; it depends only on present input and is causal. V is a linear time advance, preserving superposition, but needs a future input and is noncausal. Thus A,B. The equations completely transcribe the source block diagrams.

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