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GATE 2021 BM – Question 40

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

The shown x[n] and h[n] are convolved to give y[n]. If y[2]=1 and y[3]=0, find h[0]. The graph amplitudes are not drawn to scale.

Diagram for GATE 2021 BM question 40
  1. 1.85
  2. −2.50
  3. −1.90
  4. 2.38

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Show answer and explanation

Correct answer: (D) 2.38

Explanation

The nonzero input samples are x[1]=.1,x[2]=.5,x[3]=.4; h is supported at zero and one. Thus y[2]=.5h[0]+.1h[1]=1 and y[3]=.4h[0]+.5h[1]=0. The second equation gives h[1]=−.8h[0]. Substitution yields .42h[0]=1, so h[0]=2.38095, D.

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