Signal and System Analysis 2017 E.

Choose the correct answer for the given alternatives given below

1. Under what conditions the three signals x(t), y(t) and z(t) with period 𝑡 𝑡 and 𝑡3
respectively are periodic?
a. 𝑡1/𝑡2/𝑡3 = rational
b. All the ratios of the three periods in any order is rational
c. 𝑡1/𝑡2 is rational
d. 𝑡1/𝑡2 = 𝑡2/𝑡3
Answer: b
2. A signal is a power signal when the signal has
a. Infinite average power
b. finite average power
c. Zero average power
d. None of the Above
Answer: b
3. If a signal 𝑥(𝑡) 𝑢(𝑡) is shifted to left side by 𝑡0, then the function can be expressed as
a. 𝑥(𝑡 – 𝑡0) 𝑢(𝑡)
b. 𝑥(𝑡) 𝑢(𝑡 – 𝑡0)
c. 𝑥(𝑡 – 𝑡0) 𝑢(𝑡 – 𝑡0)
d. 𝑥(𝑡 + 𝑡0) u(t + 𝑡0)
Answer: c
4. Which one of the following is correct ? Energy of a power signal is
a. Finite
b. Zero
c. Infinite
d. none
Answer: c
5. From the following statement which one is a false statement
a. A periodic signal is a power signal if its energy content per period is finite
b. The Sum of two continuous-time periodic signals may not be periodic
c. If the signal is a random signal whose values are specified for any given time
d. The product of an even signal and an odd signal is an odd signal
e. None

6. A system is said to be shift invariant only if______

a. a shift in the input signal also results in the corresponding shift in the output
b. a shift in the input signal does not exhibit the corresponding shift in the output
c. a shifting level does not vary in an input as well as output
d. a shifting at input does not affect the output
Answer: a

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Signal and System Analysis 2017 E.C

7. Given the signal x(t), which of the following is true for signal x(2t + 8)?
a. x(t) shifted to the left by eight units
b. x(t) is compressed by a factor of 2 and then shifted left by four units
c. x(t) is expanded by a factor of 2 and then shifted right by four units
d. x(t) is reflected about the vertical axis and then shifted
Answer: b
8. The continuous time system described by the equation 𝑦(𝑡) = 𝑥(𝑡 ) comes under which
category
a. causal, linear and time varying
b. non causal, linear and time-variant
c. non causal, non-linear and time-invariant
d. causal, non-linear and time varying
Answer: b
9. A system is said to be memoryless if the output of the system depends on the
a. Past Input
b. Future Input
c. Present Input
d. Present & Future Inputs
Answer: c
10. When two systems with impulse responses h1(t) and h2(t) are connected in series, the
impulse response of the composite system is
a. h1(t) + h2(t)
b. h1(t)*h2(t),
c. h1(t)/h2(t),
d. none of the above
Answer: b
11. Which of the following express the process of ‘aliasing’?
a. Peaks overlapping
b. Phase overlapping
c. Amplitude overlapping
d. Spectral overlapping
Answer: d
12. Which among the following are the stable discrete time systems?
i. y(n) = x(4n)
ii. y(n) = x(-n)
iii. y(n) = ax(n) + 8
iv. y(n) = cos x(n)
a. i & iii
b. ii & iv
c. i, iii & iv
d. i, ii, iii & iv
Answer: d

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Signal and System Analysis 2017 E.C

13. A system is said to be casual if the output of the system depends on the
a. Past & Present Inputs
b. Present Input
c. Future Input
d. Past & Future Inputs
Answer: a
14. Determine the Time period of: 𝑥(𝑡) = 3 𝑐𝑜𝑠(20𝑡 + 5) + 𝑠𝑖𝑛(8𝑡 − 3).
a. 2/5 sec
b. 1/10 sec
c. 1/20 sec
d. 2/4 sec
Answer: a
15. A discrete signal is said to be odd or asymmetric if 𝑥(−𝑛) is equal to
a. 𝑥(−𝑛) c. – 𝑥(−𝑛)
b. 𝑥(3𝑛) d. ∞
Answer: c
16. The Fourier transform of a function is equal to its two-sided Laplace transform evaluated
a. On the real axis of the s-plane
b. On the line parallel to the real axis of the s-plane
c. On the imaginary axis of the s-plane
d. On the line parallel to the imaginary axis of the s-plane
Answer: C
17. A system is defined as
a. Any combination of components or elements that has a useful function.
b. Any combination of elements that has a single input and a single output.
c. Any closed volume for which all the inputs and outputs are known.
d. Any physical quantity that varies with time, space or any other independent variable
Answer: b
18. A system is said to be defined as non-causal, when
a) the output at the present depends on the input at an earlier time
b) the output at the present does not depend on the factor of time at all
c) the output at the present depends on the input at the current time
d) the output at the present depends on the input at a time instant in the future
Answer: d

19. The impulse response h (t) of an LTI system is given by e^(-2t) u(t). What is the step
response?
a. y(t) = 1 Ú2 (1 – e -2t) u (t)
b. y(t) = 1 Ú2 (1 – e -2t)
c. y(t) = (1- e -2t) u (t)
d. y(t) = 1 Ú2 (e-2t) u (t)
Answer: a

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Signal and System Analysis 2017 E.C

20. The difference between the highest and the lowest frequencies of a signal is known as
a. Frequency c. Bandwidth
b. Period d. Amplitude
Answer: c
21. For a band pass signal extends from 1 KHz to 2 KHz. Then the minimum sampling
frequency that needed to retain all information of the sampled signal is
a. 1 KHz. b. 2 KHz. c. 3 KHz. d. 4 KHz.
Answer: b
22. Find the Nyquist Frequency for the given signal
𝑥(𝑡) = 3 𝑐𝑜𝑠 50𝜋𝑡 + 10 𝑠𝑖𝑛 300𝜋𝑡 – 𝑐𝑜𝑠100𝜋𝑡
a. 50 Hz b. 100 Hz c. 200 Hz d. 300 Hz
Answer: d
23. Determine the Time period of: 𝑥(𝑡) = 3 𝑐𝑜𝑠(20𝑡 + 5) + 𝑠𝑖𝑛(8𝑡 − 3).
a 1/10 sec
b 1/20 sec
c 2/5 sec
d 2/4 sec
Answer: c
Explanation:

24. When x(t ) is said to be non-periodic signal?

a) If the equation x (t) = x (t + T) is satisfied for all values of T
b) If the equation x (t) = x (t + T) is satisfied for only one value of T
c) If the equation x (t) = x (t + T) is satisfied for no values of T
d) If the equation x (t) = x (t + T) is satisfied for only odd values of T
Answer: c
25. The impulse response h (t) of an LTI system is given by 𝑒 u(t). What is the step
response?
a. y(t) = 1 ⁄ 2 (1 – e − 2t) u (t)
b. y(t) = 1 ⁄ 2 (1 – e − 2t)
c. y(t) = (1 − e − 2t) u (t)
d. y(t) = 1 ⁄ 2 (e − 2t) u (t)
Answer: a
26. Fourier transform is evaluation of Laplace transform along the______ axis in s-plane.
a. Real
b. Imaginary
c. Z domain
d. S domain
Answer: b

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Signal and System Analysis 2017 E.C

27. Which of the passive component performs differentiation operation?

a) Resistor
b) Capacitor
c) Inductor
d) Amplifier
Answer: c
Explanation: Inductor performs differentiation. It is given by 𝑦 (𝑡) = 𝐿 𝑑/𝑑𝑡 𝑖(𝑡) where,
I (t) denotes current flowing through an inductor of inductance L

28. Which of the component performs integration operation?

a) Resistor
b) Diode
c) Capacitor
d) Inductor
Answer: C
Explanation: Capacitor performs integration. V (t) developed across capacitor is given by
𝑣 (𝑡) = (1/𝐶) ∗ ∫ 𝑖 (𝑡). 𝑑𝑡, I (t) is the current flowing through a capacitor of capacitance C.
29. A series RC circuit excited by voltage V is __________
a) A memory less system
b) A causal system
c) A dynamic system
d) Static system
Answer: c
30. Which of the following is a causal system?
a) y(n) = 3x(n) – 2x(n-1)
b) y(n) = 3x(n) + 2x(n+1)
c) y(n) = 3x(n+1) + 2x(n-1)
d) y(n) = 3x(n+1) + 2x(n-1) + x(n)
Answer: a
31. Which of the following statement express Fourier series?
a) The representation of periodic signals in a mathematical manner
b) The representation of non periodic signals in a mathematical manner
c) The representation of non periodic signals in terms of complex exponentials or
sinusoids
d) The representation of periodic signals in terms of complex exponentials or sinusoids
Answer: d
32. What are fourier coefficients?
a) The terms that are present in a fourier series
b) The terms that are obtained through fourier series
c) The terms which consist of the fourier series along with their sine or cosine values
d) The terms which are of resemblance to fourier transform in a fourier series
Answer: c

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Signal and System Analysis 2017 E.C

33. How does Fourier series make it easier to represent periodic signals?
a) Harmonically related
b) Periodically related
c) Sinusoidally related
d) Exponentially related
Answer: a
34. Which of the following is a condition for a signal to have a Fourier series representation?
a) The signal must be non-periodic
b) The signal must be continuous
c) The signal must be discrete
d) The signal must be complex-valued
Answer: b)
35. Which of the following is a property of the Fourier series coefficients?
a) They are real-valued
b) They are complex-valued
c) They are always positive
d) They are always negative
Answer: b
36. What is the disadvantage of exponential Fourier series?
a) It is tough to calculate
b) It is not easily visualized
c) It cannot be easily visualized as sinusoids
d) It is hard for manipulation
Answer: c
37. The Fourier series coefficient for the signal 10δ(t) is ___________
a) 1
b) 𝐶𝑜𝑠 ( k)
c) sin ( k )
d) 2
Answer: d
Explanation: X[𝑘] = ∫ 𝐴 𝛿(𝑡)𝑒 𝑑𝑡 =

Here, A=10, T=5 ∴ X[k] = 2.

38. Find the fourier transform of an exponential signal 𝑥(𝑡)= 𝑒 𝑢(𝑡), 𝑎 > 0
1
a) 𝑎+𝑗𝜔
1
b) 𝑎−𝑗𝜔
1
c) −𝑎+𝑗𝜔
d)

Answer: a

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Signal and System Analysis 2017 E.C

39. Which of the following is a reason to use the Fourier transform?

a. To analyze the frequency content of a signal
b.To filter out noise from a signal
c. To compress a signal
d.To increase the amplitude of a signal
Answer: a
40. What is the Fourier transform of a delta function?
a. A constant value
b. An impulse function
c. A sine wave
d. A cosine wave
Answer: b
41. What is the difference between the Fourier transform and the Laplace transform?
a. The Laplace transform is defined for both periodic and non-periodic signals, while
the Fourier transform is only defined for periodic signals.
b.The Laplace transform is defined for both continuous-time and discrete-time signals,
while the Fourier transform is only defined for continuous-time signals.
c. The Laplace transform is a complex function, while the Fourier transform is a real
function.
d.The Laplace transform is a time-domain representation, while the Fourier transform is
a frequency-domain representation.
Answer: b
42. What are the use of Laplace transform and Z-transform ?
a) To convert a time-domain function to a frequency-domain function
b) To convert a frequency-domain function to a time-domain function
c) To convert a power signal to an energy signal
d) To convert a continuous signal to a discrete signal
Answer: a
43. What is the Laplace transform of the unit step function u(t)?
a) 1/s
b) 1/(s^2)
c) s/(s^2 + 1)
d) 1
Answer: a

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Signal and System Analysis 2017 E.C

44. What is the Z-transform of a unit sample function δ(n)?

a) 1
b) z
c) z^-1
d) None of the above
Answer: b)
45. What is the Z-transform of the unit step function u(n)?
a) 1/(1 − 𝑧 )
b) 𝑧/(𝑧 − 1)
𝑐) (1 − 𝑧 ))/𝑧
d) None of the above
Answer: a)
46. Consider the two signals in Figure below. They are convolved to get y(t). Then the
duration of y(t) is

(a) -1 < t < 2 (b) -2 < t < 2 (c) -1 < t < 3 (d) none of the above

Answer: C

47. From the previous question, the area of y(t) is

(a) 2 (b) 4 (c) 6 (d) none of the above

Answer: a

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