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# ESE 2021 Technical Quiz 53 || Linear Time Invariant System & Sampling Theorem

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Question 1

Consider the following causal LTI system  The system is stable for what Values of Question 2

The Nyquist sampling rate for the signal S(t) = {Sin(300t)/ t}.{Sin(500t)/ t} is given by.

Question 3

Two LTI systems in cascade form as shown in below figure- If h1(n) = 3n u(n) and h2(n) = 3δ(n) – 3δ(n – 1) and If x(n) = sin(n) then output will be

Question 4

Consider the signal given below: . then the Nyquist sampling rate of the signal is

Question 5

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4.
Properties
P1: Linear but NOT time variant
P2: Time–invariant but NOT linear
P3: Linear and time–invariant
Relations
R1: y(t) = x(t)
R2: y(t) = t|x(t)|
R3: y(t) = |x(t)|
R4: y(t) = x(t–5)
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