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GATE EC 2020 || Signals & Systems || LTI Systems & Sampling Theorem Quiz 1
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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
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
. 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)
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)
Question 6
An LTI system having transfer function 
and input x(t) = sin(t +1) is in steady state. The output is sampled at a rate ω rad/s to obtain the final output {y(k)}. Which of the following is true?
and input x(t) = sin(t +1) is in steady state. The output is sampled at a rate ω rad/s to obtain the final output {y(k)}. Which of the following is true? - 449 attempts
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