# Topic: Signals and Systems (Test 3)

Topic: Signals and Systems
Q.1
Consider a signal defined by

Its Fourier Transform is
A.
B.
C.
D.
Explaination / Solution:

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Q.2
The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is

A. 0
B. 0.1
C. 1
D. 10
Explaination / Solution:

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Q.3
The value of the integral

over the contour |z| = 1, taken in the anti-clockwise direction, would be
A.
B.
C. 24/13
D. 12/13
Explaination / Solution:

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Q.4
Suppose x1(t) and x2(t) have the Fourier transforms as shown below

Which one of the following statements is TRUE?
A. x1(t) and x2(t) are complex and x1(t) x2(t) is also complex with nonzero imaginary part
B. x1(t) and x2(t) are real and x1(t) x2(t) is also real
C. x1(t) and x2(t) are complex but x1(t) x2(t) is real
D. x1(t) and x2(t) are imaginary but x1(t) x2(t) is real
Explaination / Solution:

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Q.5
The impulse response h(t) of a linear time invariant continuous time system is described by   where u(-t) denotes the unit step function, and α  and β are real constants. This system is stable if
A. α is positive and β is positive
B. α is negative and β is negative
C. α is negative and β is negative
D. α is negative and β is positive
Explaination / Solution:

This system is stable only when bounded input has bounded output For stability αt < 0 for t > 0 that implies α < 0 and βt > 0 for t > 0 that implies β  > 0. Thus, α is negative and β is positive.

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Q.6
Let f(x) be a real, periodic function satisfying f(−x) = −f(x). The general form of its Fourier series representation would be
A.
B.
C.
D.
Explaination / Solution:

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Q.7
A discrete time linear shift - invariant system has an impulse response h[n] with h[0] = 1,h[1] =- 1,h[2] = 2, and zero otherwise The system is given an input sequence x[n] with x[0] = x[2] = 1, and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are respectively
A. 5, 2
B. 6, 2
C. 6, 1
D. 5, 3
Explaination / Solution:

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Q.8
Let z(t) = x(t) * y(t), where "*" denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).
A. c.x(ct) * y(ct)
B. x(ct) * Y(ct)
C. c.x(t) * y(ct)
D. c.x(ct) * y(t)
Explaination / Solution:

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Q.9
The Fourier series of a real periodic function has only (P) cosine terms if it is even (Q) sine terms if it is even (R) cosine terms if it is odd (S) sine terms if it is odd Which of the above statements are correct ?
A. P and S
B. P and R
C. Q and S
D. Q and R
Explaination / Solution:

The Fourier series of a real periodic function has only cosine terms if it is even and sine terms if it is odd.

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Q.10
For a periodic signal  the fundamental frequency in radians/s is
A. 100
B. 300
C. 500
D. 1500