# Topic: Signals and Systems (Test 2)

Topic: Signals and Systems
Q.1
The fourier series expansion  of the periodic signal shown below will contain the following nonzero terms

A.
B.
C.
D.
Answer : Option D
Explaination / Solution:

⇒ it satisfies the half wave symmetry, so that it contains only odd harmonics.
⇒ It satisfies the even symmetry. So bn = 0

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Q.2
The frequency response of a linear, time-invariant system is given by  The step response of the system is
A. 5(1 - e-5t) u(t)
B. 5(1 - e-t/5) u(t)
C. 1/2 (1 - e-5t) u(t)
D. 1/5 (1 - e-t/5) u(t)
Answer : Option B
Explaination / Solution:

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Q.3
A function y(t), such that y(0) = 1 and y(1) = 3e-1, is a solution of the differential equation  Then y(2) is
A. 5e-1
B. 5e-2
C. 7e-1
D. 7e-2
Answer : Option B
Explaination / Solution:

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Q.4
The response h(t) of a linear time invariant system to an impulse δ(t) , under initially relaxed condition is  The response of this system for a unit step input u(t) is
A.
B.
C.
D.
Answer : Option C
Explaination / Solution:

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Q.5
The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system ?
A. y(t) = x(t - 2) + x(t + 4)
B. y(t) = (t - 4)x(t + 1)
C. y(t) = (t + 4)x(t - 1)
D. y(t) = (t + 5)x(t + 5)
Answer : Option C
Explaination / Solution:

The output of causal system depends only on present and past states only. In option (A) y(0) depends on x(- 2) and x(4). In option (B) y(0) depends on x(1). In option (C) y(0) depends on x(- 1). In option (D) y(0) depends on x(5). Thus only in option (C) the value of y(t) at t = 0 depends on x(- 1) past value. In all other option present value depends on future value.

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Q.6
Given that f(y) = | y | / y, and q is any non-zero real number, the value of | f(q) - f(-q) | is
A. 0
B. -1
C. 1
D. 2
Answer : Option D
Explaination / Solution:

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Q.7
The signal x(t) is described by

Two of the angular frequencies at which its Fourier transform becomes zero are
A. π, 2π
B. 0.5π, 1.5π
C. 0, π
D. 2π, 2.5π
Answer : Option A
Explaination / Solution:

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Q.8
Group I lists a set of four transfer functions. Group II gives a list of possible step response y(t). Match the step responses with the corresponding transfer functions.

A. P - 3,Q - 1,R - 4,S - 2
B. P - 3,Q - 2,R - 4,S - 1
C. P - 2,Q - 1,R - 4,S - 2
D. P - 3,Q - 4,R - 1,S - 2
Answer : Option D
Explaination / Solution:

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Q.9
Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
A.  product of h1(t)  and h2(t)
B.  sum of h1(t)  and h2(t)
C.  Convolution of h1(t)  and h2(t)
D.  Subtraction  of h1(t)  and h2(t)
Answer : Option C
Explaination / Solution:

If the two systems with impulse responseh1(t)  and h2(t)   are connected in cascaded configuration as shown in figure, then the overall response of the system is the convolution of the individual impulse responses.

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Q.10
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is
A. 5
B. 12
C. 15
D. 20
Answer : Option A
Explaination / Solution:
No Explaination.

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