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Test: Chebyshev Filters - 2


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10 Questions MCQ Test Signals and Systems | Test: Chebyshev Filters - 2

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

 What is the value of |TN(±1)|? 

Detailed Solution for Test: Chebyshev Filters - 2 - Question 1

Explanation: We know that a chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
Thus |TN(±1)|=1.

Test: Chebyshev Filters - 2 - Question 2

The chebyshev polynomial is oscillatory in the range |x|<∞.

Detailed Solution for Test: Chebyshev Filters - 2 - Question 2

Explanation: The chebyshev polynomial is oscillatory in the range |x|≤1 and monotonic outside it.

Test: Chebyshev Filters - 2 - Question 3

If NB and NC are the orders of the Butterworth and Chebyshev filters respectively to meet the same frequency specifications, then which of the following relation is true? 

Detailed Solution for Test: Chebyshev Filters - 2 - Question 3

Explanation: The equi-ripple property of the chebyshev filter yields a narrower transition band compared with that obtained when the magnitude response is monotone. As a consequence of this, the order of a chebyshev filter needed to achieve the given frequency domain specifications is usually lower than that of a Butterworth filter.

Test: Chebyshev Filters - 2 - Question 4

 The chebyshev-I filter is equi-ripple in pass band and monotonic in the stop band.

Detailed Solution for Test: Chebyshev Filters - 2 - Question 4

Explanation: There are two types of chebyshev filters. The Chebyshev-I filter is equi-ripple in the pass band and monotonic in the stop band and the chebyshev-II filter is quite opposite.

Test: Chebyshev Filters - 2 - Question 5

What is the equation for magnitude frequency response |H(jΩ)| of a low pass chebyshev-I filter?

Detailed Solution for Test: Chebyshev Filters - 2 - Question 5

Explanation: The magnitude frequency response of a low pass chebyshev-I filter is given by

where ϵ is a parameter of the filter related to the ripple in the pass band and TN(x) is the Nth order chebyshev polynomial.

Test: Chebyshev Filters - 2 - Question 6

 What is the number of minima’s present in the pass band of magnitude frequency response of a low pass chebyshev-I filter of order 4?

Detailed Solution for Test: Chebyshev Filters - 2 - Question 6

Explanation: In the magnitude frequency response of a low pass chebyshev-I filter, the pass band has 2 maxima and 2 minima(order 4=2 maxima+2 minima).

Test: Chebyshev Filters - 2 - Question 7

What is the number of maxima present in the pass band of magnitude frequency response of a low pass chebyshev-I filter of order 5?

Detailed Solution for Test: Chebyshev Filters - 2 - Question 7

Explanation: In the magnitude frequency response of a low pass chebyshev-I filter, the pass band has 3 maxima and 2 minima(order 5=3 maxima+2 minima).

Test: Chebyshev Filters - 2 - Question 8

 The sum of number of maxima and minima in the pass band equals the order of the filter.

Detailed Solution for Test: Chebyshev Filters - 2 - Question 8

Explanation: In the pass band of the frequency response of the low pass chebyshev-I filter, the sum of number of maxima and minima is equal to the order of the filter.

Test: Chebyshev Filters - 2 - Question 9

The poles of HN(s).HN(-s) are found to lie on:

Detailed Solution for Test: Chebyshev Filters - 2 - Question 9

Explanation: The poles of HN(s).HN(-s) is given by the characteristic equation 1+ϵ2TN2(s/j)=0.
The roots of the above characteristic equation lies on ellipse, thus the poles of HN(s).HN(-s) are found to lie on ellipse.

Test: Chebyshev Filters - 2 - Question 10

If the discrimination factor ‘d’ and the selectivity factor ‘k’ of a chebyshev I filter are 0.077 and 0.769 respectively, then what is the order of the filter?

Detailed Solution for Test: Chebyshev Filters - 2 - Question 10

Explanation: We know that the order of a chebyshev-I filter is given by the equation,
N=cosh-1(1/d)/cosh-1(1/k)=4.3
Rounding off to the next large integer, we get N=5.

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