Signal Processing MCQ Questions & Answers

51

Match List-I with List-II and select the correct answer using the options given below:

List-I (x[n])	List-II (X(z))
a. $${a^n}u\left[ n \right]$$	1. $$\frac{{az}}{{{{\left( {z - a} \right)}^2}}}$$
b. $${a^{n - 2}}u\left[ {n - 2} \right]$$	2. $$\frac{{z{e^{ - j}}}}{{z{e^{ - j}} - a}}$$
c. $${e^{jn}}{a^n}$$	3. $$\frac{z}{{z - a}}$$
d. $$n.{a^n}u\left[ n \right]$$	4. $$\frac{{{z^{ - 1}}}}{{z - a}}$$

A) a-3, b-2, c-4, d-1 B) a-2, b-3, c-4, d-1 C) a-3, b-4, c-2, d-1 D) a-1, b-4, c-2, d-3

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Answer & Solution

Answer: Option C

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52

The minimum number of delay elements required in realizing a digital filter with the transfer function $$H\left( z \right) = \frac{{1 + a{z^{ - 1}} + b{z^{ - 2}}}}{{1 + c{z^{ - 1}} + d{z^{ - 2}} + e{z^{ - 3}}}}$$ is

A) 2 B) 3 C) 4 D) 5

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Answer & Solution

Answer: Option B

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53

An input x[n] with length 3 is applied to a linear time invariant system having an impulse response h[n] of length 5 and Y(ω) is the DTFT of the output y[n] of the system. If |h[n]| ≤ L and |x[n]| ≤ L for all n, the maximum value of Y(0) can be:

A) 15 LB B) 12 LB C) 8 LB D) 7 LB

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Answer & Solution

Answer: Option D

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54

The complex exponential power form of Fourier series of x(t) is: $$x\left( t \right) = \sum\nolimits_{k = - \infty }^\infty {{a_k}.{e^{j\frac{{2\pi }}{{{T_0}}}.kt}}} $$
If $$x\left( t \right) = \sum\nolimits_{b = - \infty }^\infty \delta \left( {t - b} \right),$$ then the value of ak is:

A) 1 - (-1)^k B) 1 + (-1)^k C) 1 D) -1

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Answer & Solution

Answer: Option C

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55

If x(t) = 10 rect $$\left( {\frac{{\text{t}}}{2}} \right),$$ the zero-frequency value of its spectrum is given by

A) 10 B) 5 C) 2 D) 20

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Answer & Solution

Answer: Option A

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56

FIR filters can be designed using

A) windowing method B) bilinear transformation C) impulse invariant transformation D) windowing and frequency sampling method

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Answer & Solution

Answer: Option D

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57

The auto correlation function R_x(τ) satisfies which one of the following properties?

A) R_x(τ) = -R_x(-τ) B) R_x(τ) = R_x(-τ) C) R_x(τ) ≥ R_x(0) D) R_x(τ) ≥ 1

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Answer & Solution

Answer: Option B

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58

If a random process X(t) is ergodic then, statistical averages

A) and time averages are different B) and time averages are same C) are greater than time averages D) are smaller than time averages

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Answer & Solution

Answer: Option B

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59

Which one of the following systems described by the following input-output relation is non-linear?

A) y(n) = nx(2n) B) y(n) = x(n²) C) y(n) = n²x(n) D) y(n) = x²(n)

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Answer & Solution

Answer: Option D

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60

Let h(t) denote the impulse response of a causal system with transfer function $$\frac{1}{{{\text{s}} + 1}}.$$ Consider the following three statements:
S₁: The system is stable.
S₂: $$\frac{{{\text{h}}\left( {{\text{t}} + 1} \right)}}{{{\text{h}}\left( {\text{t}} \right)}}$$ is independent of t for t > 0.
S₃: A non-causal system with the same transfer function is stable.
For the above system,

A) only S₁ and S₂ are true B) only S₂ and S₃ are true C) only S₁ and S₃ are true D) S₁, S₂ and S₃ are true

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Answer & Solution

Answer: Option A

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Signal Processing MCQ Questions & Answers | ECE