Direction: A continuous time signal X(t) has Fourier transform
| X(jω) = | 1 + ω2 |
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Calculate y(t) = d2 x(t – 1) dt2
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ejω ω5 1 + ω2 -
ejω·ω 1 + ω2 -
– je-jω·ω5 1 + ω2 -
– ejω·ω 1 + ω2
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Correct Option: C
If x(t) ← F.T.→ X(jω)
| then | x(t) ←F.T.→ jω X(jω) | dx |
| and | x(t) ←F.T.→ (jω)2 X(jω) | dt2 |
| and | x(t – 1) ←F.T.→ (jω)2 X(jω) e– jω | dt2 |
| Therefore, Y(jω) = – ω2· | 1 + ω2 |
| or Y(jω) = | 1 + ω2 |
Hence, alternative (C) is the correct choice.
