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Test: FIR Differentiator Design - Electrical Engineering (EE) MCQ


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15 Questions MCQ Test - Test: FIR Differentiator Design

Test: FIR Differentiator Design for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Test: FIR Differentiator Design questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: FIR Differentiator Design MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: FIR Differentiator Design below.
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Test: FIR Differentiator Design - Question 1

How is the frequency response of an ideal differentiator related to the frequency?

Detailed Solution for Test: FIR Differentiator Design - Question 1

Explanation: An ideal differentiator has a frequency response that is linearly proportional to the frequency.

Test: FIR Differentiator Design - Question 2

Which of the following is the frequency response of an ideal differentiator, Hd(ω)?

Detailed Solution for Test: FIR Differentiator Design - Question 2

Explanation: An ideal differentiator is defined as one that has the frequency response
Hd(ω)= jω ; -π ≤ ω ≤ π.

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Test: FIR Differentiator Design - Question 3

What is the unit sample response corresponding to Hd(ω)?

Detailed Solution for Test: FIR Differentiator Design - Question 3

Explanation: We know that, for an ideal differentiator, the frequency response is given as
Hd(ω)= jω ; -π ≤ ω ≤ π
Thus, we get the unit sample response corresponding to the ideal differentiator is given as
h(n)=cosπn/n.

Test: FIR Differentiator Design - Question 4

The ideal differentiator ahs which of the following unit sample response?

Detailed Solution for Test: FIR Differentiator Design - Question 4

Explanation: We know that the unit sample response of an ideal differentiator is given as
h(n)=cosπn/n
So, we can state that the unit sample response of an ideal differentiator is anti-symmetric because cos⁡πn is also an anti-symmetric function.

Test: FIR Differentiator Design - Question 5

If hd(n) is the unit sample response of an ideal differentiator, then what is the value of hd(0)? 

Detailed Solution for Test: FIR Differentiator Design - Question 5

Explanation: Since we know that the unit sample response of an ideal differentiator is anti-symmetric,
=>hd(0)=0.

Test: FIR Differentiator Design - Question 6

 In this section, we confine our attention to FIR designs in which h(n)=-h(M-1-n).

Detailed Solution for Test: FIR Differentiator Design - Question 6

Explanation: In view of the fact that the ideal differentiator has an anti-symmetric unit sample response, we shall confine our attention to FIR designs in which h(n)=-h(M-1-n).

Test: FIR Differentiator Design - Question 7

Which of the following is the condition that an differentiator should satisfy?

Detailed Solution for Test: FIR Differentiator Design - Question 7

Explanation: For an FIR filter, when M is odd, the real valued frequency response of the FIR filter Hr(ω) has the characteristic that Hr(0)=0. A zero response at zero frequency is just the condition that the differentiator should satisfy.

Test: FIR Differentiator Design - Question 8

Full band differentiators can be achieved with an FIR filters having odd number of coefficients. 

Detailed Solution for Test: FIR Differentiator Design - Question 8

Explanation: Full band differentiators cannot be achieved with an FIR filters having odd number of coefficients, since Hr(π)=0 for M odd.

Test: FIR Differentiator Design - Question 9

 If fp is the bandwidth of the differentiator, then the desired frequency characteristic should be linear in the range: 

Detailed Solution for Test: FIR Differentiator Design - Question 9

Explanation: In most cases of practical interest, the desired frequency response characteristic need only be linear over the limited frequency range 0 ≤ ω ≤ 2πfp , where fp is the bandwidth of the differentiator.

Test: FIR Differentiator Design - Question 10

What is the desired response of the differentiator in the frequency range 2πfp ≤ ω ≤ π? 

Detailed Solution for Test: FIR Differentiator Design - Question 10

Explanation: In the frequency range 2πfp ≤ ω ≤ π, the desired response may be either left unconstrained or constrained to be zero.

Test: FIR Differentiator Design - Question 11

What is the weighting function used in the design of FIR differentiators based on the chebyshev approximation criterion?

Detailed Solution for Test: FIR Differentiator Design - Question 11

Explanation: In the design of FIR differentiators based on the chebyshev approximation criterion, the weighting function W(ω) is specified in the program as
W(ω)=1/ω
in order that the relative ripple in the pass band be a constant.

Test: FIR Differentiator Design - Question 12

 The absolute error between the desired response ω and the approximation Hr(ω) decreases as ω varies from 0 to 2πfp.

Detailed Solution for Test: FIR Differentiator Design - Question 12

Explanation: We know that the weighting function is
W(ω)=1/ω
in order that the relative ripple in the pass band be a constant. Thus, the absolute error between the desired response ω and the approximation Hr(ω) increases as ω varies from 0 to 2πfp.

Test: FIR Differentiator Design - Question 13

Which of the following is the important parameter in a differentiator?

Detailed Solution for Test: FIR Differentiator Design - Question 13

Explanation: The important parameters in a differentiator are its length, its bandwidth and the peak relative error of the approximation. The inter relationship among these three parameters can be easily displayed parametrically.

Test: FIR Differentiator Design - Question 14

In this section, we confine our attention to FIR designs in which h(n)=h(M-1-n).

Detailed Solution for Test: FIR Differentiator Design - Question 14

Explanation: In view of the fact that the ideal differentiator has an anti-symmetric unit sample response, we shall confine our attention to FIR designs in which h(n)=-h(M-1-n).

Test: FIR Differentiator Design - Question 15

What is the maximum value of fp with which good designs are obtained for M odd? 

Detailed Solution for Test: FIR Differentiator Design - Question 15

Explanation: Designs based on M odd are particularly poor if the bandwidth exceeds 0.45. The problem is basically the zero in the frequency response at ω=π(f=1/2). When fp <0.45, good designs are obtained for M odd.

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