Signal Processing MCQ Questions & Answers

31

A periodic signal x(t) has a trigonometric Fourier series expansion
$$x\left( t \right) = {a_0} + \sum\limits_{n = 1}^\infty {\left( {{a_n}\,\cos \,n{\omega _0}t + {b_n}\sin \,n{\omega _0}t} \right)} $$
If $$x\left( t \right) = - x\left( { - t} \right) = - x\left( {{{t - \pi } \over {{\omega _0}}}} \right),$$ we can conclude that

A) a_n are zero for all n and b_n are zero for n even B) a_n are zero for all n and b_n are zero for n odd C) a_n are zero for n even and b_n are zero for n odd D) a_n are zero for n odd and b_n are zero for n even

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Answer & Solution

Answer: Option A

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32

If $$F\left( s \right) = L\left| {f\left( t \right)} \right| = {K \over {\left( {s + 1} \right)\left( {{s^2} + 4} \right)}},$$ then $$\mathop {\lim }\limits_{t \to \infty } f\left( t \right)$$ is given by

A) $${K \over 4}$$ B) Zero C) Infinite D) Undefined

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Answer & Solution

Answer: Option C

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33

The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by
$$y\left( t \right) = \left( {{1 \over {100}}} \right)\cos \left( {100t - {{10}^{ - 6}}} \right)\cos \left( {{{10}^6}t - 1.56} \right)$$
The group delay (t_g) and the phase delay (t_p) in seconds, of the channel are

A) t_g = 10^-6, t_p = 1.56 B) t_g = 1.56, t_p = 10^-6 C) t_g = 10^-8, t_p = 1.56 × 10^-6 D) t_g = 10⁸, t_p = 1.56

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Answer & Solution

Answer: Option D

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34

Let x(t) be the input to a linear, time-invariant system. The required output is 4x(t - 2). The transfer function of the system should be

A) 4e^j4πf B) 2e^-j8πf C) 4e^-j4πf D) 2e^j8πf

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Answer & Solution

Answer: Option C

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35

Let y[n] denote the convolution of h[n] and g[n], where h[n] = $${\left( {\frac{1}{2}} \right)^n}$$ u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = $$\frac{1}{2},$$ then g[1] equals

A) 0 B) $${1 \over 2}$$ C) 1 D) $${3 \over 2}$$

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Answer & Solution

Answer: Option A

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36

The trigonometric Fourier series of an even function of time does not have

A) The dc term B) Cosine terms C) Sine terms D) Odd harmonic terms

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Answer & Solution

Answer: Option C

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37

The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude
Signal Processing mcq question image

A) h[n] is real for all n B) h[n] is purely imaginary for all n C) h[n] is real for only even n D) h[n] is purely imaginary for only odd n

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Answer & Solution

Answer: Option A

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38

Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P₁, P₂ and P₃ with system relations R₁, R₂, P₃, P₄.
Properties
P₁ : Linear but NOT time-invariant
P₂ : Time-invariant but NOT linear
P₃ : Linear and time-invariant
Relations
R₁ : y(t) = t²x(t)
R₂ : y(t) = t |x(t)|
R₃ : y(t) = |x(t)|
R₄ : y(t) = x(t - 5)

A) (P₁, R₁), (P₂, R₃), (P₃, R₄) B) (P₁, R₂), (P₂, P₃), (P₃, R₄) C) (P₁, R₃), (P₂, R₁), (P₃, R₂) D) (P₁, R₁), (P₂, R₂), (P₃, R₃)

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Answer & Solution

Answer: Option B

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39

The z-transform of the following real exponential sequence
x(nT) = aⁿ, nT ≥ 0
= 0, nT < 0, a > 0

A) $${1 \over {1 - {z^{ - 1}}}};\left| z \right| > 1$$ B) $${1 \over {1 - a{z^{ - 1}}}};\left| z \right| > a$$ C) 1 for all z D) $${1 \over {1 - a{z^{ - 1}}}};\left| z \right| < a$$

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Answer & Solution

Answer: Option B

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40

Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
$$y\left[ n \right] = \left\{ {\matrix{ {n\left| {x\left[ n \right]} \right|,} & {{\rm{for}}\,0 \le n \le 10} \cr {x\left[ n \right] - x\left[ {n - 1} \right],} & {{\rm{otherwise}}} \cr } } \right.$$
Which one of the following statements is true about the system?

A) It is causal and stable B) It is causal but not stable C) It is not causal but stable D) It is neither causal nor stable

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Answer & Solution

Answer: Option A

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Signal Processing MCQ Questions & Answers | ECE