GATE EC 2015 Set 1 — Question 27
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Signals & Systems → Continuous-Time Signals → Shifting, Convolution & Modulation
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Question
The result of the convolution is
Correct answer
(D) x(-t - t₀)
Solution
The convolution of a signal with an impulse is .
Here, we have .
Recall that the Dirac delta function is even: .
Thus, .
Now, let . The convolution is:Substituting into , we get:Therefore, the correct option is (D).
Here, we have .
Recall that the Dirac delta function is even: .
Thus, .
Now, let . The convolution is:Substituting into , we get:Therefore, the correct option is (D).
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