GATE 2022 : Signals & Systems- 39 (App update required to attempt this test)

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Question 1

Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ⊗ h(t) = y(t). Further, if |x(t)| ⊗ | y(t)| = z(t), which of the following statement is true?

• AFor some but not all t ϵ (–∞, 0), z(t) < y(t)
• BFor all t ϵ (–∞, ∞), Z(t) > y(t).
• CFor some but not all t ϵ(–∞, ∞) Z(t) > y(t)
• DFor all t ϵ (–∞, ∞), Z ≤ y(t)

Question 2

The impulse response of two systems are given below,


Which of the following is an LTI system?

• A only
• B only
• CBoth and
• DNone

Question 3

Compute the output y(t) for a continuous time LTI system whose impulse response h(t) and the input x(t) are given by
h(t) = e^–αt u(t) , x(t) = e^αt u(–t) α > 0

• A
• B
• C
• D

Question 4

Consider a system with U(t) as input and V(t) as output

Choose the correct option

• AThe system is nonlinear
• BSystem is time invariant
• CThe system is stable
• DThe system has memory

Question 5

The unilateral Laplace transform of a signal x(t) is

If x(t) be (e^–at – ate^–t) U(t) then value of a is

Answer

Question 6

The Fourier transform of a signal h(t) is H(jω) = (2cosω)(sin2ω)/ω. The value of h(0) is

Answer

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