Signal Processing MCQ Questions & Answers

21

Which of the following gives the average value or expectation of the function g(X) of the random variable X?
(Given f(X) is the probability density function)

A) $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {g\left( X \right)dx} $$ B) $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {g\left( X \right)f\left( X \right)dx} $$ C) $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {{g^ * }\left( X \right)dx} $$ D) $$E\left[ {g\left( X \right)} \right] = \int\limits_{ - \infty }^\infty {\frac{{g\left( X \right)}}{{f\left( X \right)}}dx} $$

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Answer & Solution

Answer: Option B

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22

Consider the following statements regarding filters:
1. Cauer filter has equiripple passband and stopband.
2. For a given filter order, passband and stopband deviations, Cauer filters have more transition bandwidth as compared to Chebyshev filters.
3. Linear phase characteristics cannot be achieved in IIR filters.
Which of the above statements are correct?

A) 1 and 2 only B) 1 and 3 only C) 2 and 3 only D) 1, 2 and 3

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Answer & Solution

Answer: Option B

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23

Z-transform deals with discrete time systems for their:
1. Transient behavior
2. Steady-state behavior
Which of the above behaviors is/are correct?

A) 1 only B) 2 only C) Both 1 and 2 only D) Neither 1 nor 2

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Answer & Solution

Answer: Option C

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24

A signal x(n) = sin(ω₀ n + φ) is the input to a linear time-invariant system having a frequency response H(e^jω). If the output of the system Ax(n - n₀), then the most general form of ∠H(e^jω) will be

A) -n₀ω₀ + β for any arbitrary real β B) -n₀ω₀ + 2πk for any arbitrary integer k C) n₀ω₀ + 2πk for any arbitrary integer k D) -n₀ω₀φ

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Answer & Solution

Answer: Option B

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25

Which one of the following system is nonlinear? [y(t) = output; x(t) = input]

A) y(t) = 2x(t - 1) - 3x(t - 2) + x(t - 3) B) y(t) = 5x(t) C) y(t) = 2x(t - 1) - x(t - 2) - x(t - 4) D) y(t) = 2x(t) + 3.6

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Answer & Solution

Answer: Option D

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26

What is the Fourier Inverse of $$H\left( f \right) = \frac{{j3\pi f}}{{1 + j\pi f}}?$$

A) 3e^-tu(t) B) 3δ(t) - 6e^-2tu(t) C) 6e^-2tu(t) D) 3 - 6e^-2tu(t)

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Answer & Solution

Answer: Option B

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27

Which one of the following digital filters does have a linear phase response?

A) y(n) + y(n - 1) = x(n) - x(n - 1) B) y(n) = $$\frac{1}{6}$$ [3x(n) + 2x(n - 1) + 3x(n - 2)] C) y(n) = $$\frac{1}{6}$$ [x(n) + 2x(n - 1) + 3x(n - 2)] D) y(n) = $$\frac{1}{4}$$ [x(n) + 2x(n - 1) + x(n - 2)]

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Answer & Solution

Answer: Option D

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28

A first order system initially at rest has for a signal u(t), the response 1 - e^-t. If the signal is 2u(t) cost, the response will be

A) $$\sqrt 2 \cos \left( {t - \frac{\pi }{4}} \right) - {e^{ - t}}$$ B) $$\sqrt 2 \cos \left( {t - \frac{\pi }{4}} \right) - \frac{1}{2}{e^{ - t}}$$ C) $$2\left( {1 - {e^{ - t}}} \right) + \frac{1}{{\sqrt 2 }}\cos \left( {t - \frac{\pi }{4}} \right)$$ D) $$\sqrt 2 \cos \left( {t\frac{\pi }{4}} \right)$$

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Answer & Solution

Answer: Option A

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29

Consider a signal x(t) such that x(-t) = x(t). Let X(ω) be the Fourier transform of x(t). Then, X(ω) satisfies the property

A) X(ω) = X(-ω) B) X(ω) = -X*(ω) C) X(ω) = X*(ω) D) X(ω) = X*(-ω)

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Answer & Solution

Answer: Option A

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30

The covariance function of a band limited white noise is

A) A Dirace delta function B) An exponentially decreasing function C) A sinc function D) A sinc² function

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Answer & Solution

Answer: Option C

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Signal Processing MCQ Questions & Answers | ECE