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Test: Discrete Time Signal Analysis - 2


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15 Questions MCQ Test Digital Signal Processing | Test: Discrete Time Signal Analysis - 2

Test: Discrete Time Signal Analysis - 2 for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: Discrete Time Signal Analysis - 2 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Discrete Time Signal Analysis - 2 MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Discrete Time Signal Analysis - 2 below.
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Test: Discrete Time Signal Analysis - 2 - Question 1

Which of the following relation is true if the signal x(n) is real?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 1

Explanation: We know that,

Test: Discrete Time Signal Analysis - 2 - Question 2

 For a signal x(n) to exhibit even symmetry, it should satisfy the condition | X(-ω)|=| X(ω)|. 

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 2

Explanation: We know that, if a signal x(n) is real, then
X*(ω)=X(-ω)
If the signal is even symmetric, then the magnitude on both the sides should be equal.
So, |X*(ω)|=|X(-ω)| =>| X(-ω)|=| X(ω)|.

Test: Discrete Time Signal Analysis - 2 - Question 3

What is the energy density spectrum Sxx(ω) of the signal x(n)=anu(n), |a|<1?  

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 3

Explanation: Since |a|<1, the sequence x(n) is absolutely summable, as can be verified by applying the geometric summation formula.

Test: Discrete Time Signal Analysis - 2 - Question 4

 What is the Fourier transform of the signal x(n) which is defined as shown in the graph below?

None of the mentioned

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 4

Explanation: The Fourier transform of this signal is

Test: Discrete Time Signal Analysis - 2 - Question 5

Which of the following condition is to be satisfied for the Fourier transform of a sequence to be equal as the Z-transform of the same sequence?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 5

Explanation: Let us consider the signal to be x(n)

Test: Discrete Time Signal Analysis - 2 - Question 6

The sequencedoes not have both z-transform and Fourier transform.

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 6

Explanation: The given x(n) do not have Z-transform. But the sequence have finite energy. So, the given sequence x(n) has a Fourier transform.

Test: Discrete Time Signal Analysis - 2 - Question 7

If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as:

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 7

Explanation: Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)
=> cx(z)= X-1(ln X(z))

Test: Discrete Time Signal Analysis - 2 - Question 8

 If cx(n) is the complex cepstrum sequence obtained from the inverse Fourier transform of ln X(ω), then what is the expression for cθ(n)?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 8

Explanation: We know that,

Test: Discrete Time Signal Analysis - 2 - Question 9

What is the Fourier transform of the signal x(n)=u(n)?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 9

 

Explanation: Given x(n)=u(n)
We know that the z-transform of the given signal isROC:|z|>1
X(z) has a pole p=1 on the unit circle, but converges for |z|>1.
If we evaluate X(z) on the unit circle except at z=1, we obtain

Test: Discrete Time Signal Analysis - 2 - Question 10

 If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as:

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 10

Explanation: We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.

Test: Discrete Time Signal Analysis - 2 - Question 11

What are the main characteristics of Anti aliasing filter?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 11

Explanation: T he anti aliasing filter is an analog filter which has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an anti aliasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wide band and exceeds the bandwidth of the desired signal.

Test: Discrete Time Signal Analysis - 2 - Question 12

In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system. 

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 12

Explanation: Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

Test: Discrete Time Signal Analysis - 2 - Question 13

The term ‘bandwidth’ represents the quantitative measure of a signal. 

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 13

Explanation: In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.

Test: Discrete Time Signal Analysis - 2 - Question 14

 

If F1 and F2 are the lower and upper cutoff frequencies of a band pass signal, then what is the condition to be satisfied to call such a band pass signal as narrow band signal?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 14

Explanation: If the difference in the cutoff frequencies is much less than the mean frequency, the such a band pass signal is known as narrow band signal.

Test: Discrete Time Signal Analysis - 2 - Question 15

What is the frequency range(in Hz) of Electroencephalogram(EEG)?

Detailed Solution for Test: Discrete Time Signal Analysis - 2 - Question 15

Explanation: Electroencephalogram(EEG) signal has a frequency range of 0-100 Hz.

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