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GATE EC 2020 National Champion Quiz 1 : Signal & Systems (App update required to attempt this test)
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Question 1
Represent the following signal as sum of its singularities:
Question 2
If the transfer function of a system is 
find the impulse response of the system for |z|>2.
find the impulse response of the system for |z|>2. Question 3
Consider the function f(t) having Laplace transform
The final value of f(t) would be:
The final value of f(t) would be:
Question 4
Let f(x) be a real, periodic function adequate the condition f (-x) = -f(x). The general form of its Fourier series representation would be
Question 5
A continuous time system has input and output x (t) and y (t) respectively. The system is defined by its input output relation y (t) = x (t2). The system is
Question 6
If y(t) is the Hilbert Transform of 
, where
, where
Then find the value of
Question 7
A casual LTI system is described by the difference equation 3y[n] = αy [n-2] – 3x[n] + βx [n-2]. The system is stable only if
Question 8
Two sequences x1 [n] and x2 [n] have the same energy. Suppose x1[n] = a 0.5n u[n], where a is a positive real number and u[n] is the unit step sequence. Assume
Then the value of a is__________.
Then the value of a is__________.
Question 9
The following five facts are given about a discrete time signal 
with z-transform 
.
1)
is a real right sided signal
2)
has exactly two poles
3)
has two zeros at the origin
4)
has a pole at 
5)
Then,
?
with z-transform . 1)
is a real right sided signal 2)
has exactly two poles 3)
has two zeros at the origin 4)
has a pole at 5)
Then,
?Question 10
Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)n u[n] and g[n] is a causal sequence. If y[0] =1 and y [1] = ½, then g[1] equals
Question 11
DFT of a real valued signal x(n) is {10, 2+3j, α, 3-j, -3, β, 1+2j, γ}.
Find the energy of the signal.
Question 12
Let the signal 
be a discrete time signal represented as
This signal is passed through a system whose impulse response is represented as
. The minimum value of 
so that 
is _______ Hz
be a discrete time signal represented as This signal is passed through a system whose impulse response is represented as
. The minimum value of so that is _______ Hz - 769 attempts
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Nov 20ESE & GATE EC
