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# GATE EC 2022: Signals & Systems Quiz 3 (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?

Question 2

Let y(t) =[u(t)]*(t-3k) such that, y(t)=A for 0t<3, determine the value of A

Question 3

The impulse response of two systems are given below,

Which of the following is an LTI system?

Question 4

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) = eαt u(–t) α > 0

Question 5

Find the system’s response to the input x(t)= if the unit impulse response h(t) of a DT LTI system is h(t) = u(-t+1) use convolution?

Question 6

x(t) is nonzero only for Tx< t < T'x , and similarly, y(t) is nonzero only for Ty< t < T'y. Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?
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