Test: FIR Differentiator Design

# Test: FIR Differentiator Design

Test Description

## 15 Questions MCQ Test Signals and Systems | Test: FIR Differentiator Design

Test: FIR Differentiator Design for Electrical Engineering (EE) 2022 is part of Signals and Systems 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) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: FIR Differentiator Design below.
Solutions of Test: FIR Differentiator Design questions in English are available as part of our Signals and Systems for Electrical Engineering (EE) & Test: FIR Differentiator Design solutions in Hindi for Signals and Systems course. Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free. Attempt Test: FIR Differentiator Design | 15 questions in 15 minutes | Mock test for Electrical Engineering (EE) preparation | Free important questions MCQ to study Signals and Systems for Electrical Engineering (EE) Exam | Download free PDF with solutions
 1 Crore+ students have signed up on EduRev. Have you?
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.

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.

## Signals and Systems

32 videos|76 docs|64 tests
 Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code
Information about Test: FIR Differentiator Design Page
In this test you can find the Exam questions for Test: FIR Differentiator Design solved & explained in the simplest way possible. Besides giving Questions and answers for Test: FIR Differentiator Design, EduRev gives you an ample number of Online tests for practice

## Signals and Systems

32 videos|76 docs|64 tests