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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Tests  >  Signals and Systems  >  Test: Backward Difference Method - Electronics and Communication Engineering (ECE) MCQ

Test: Backward Difference Method - Electronics and Communication Engineering (ECE) MCQ


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10 Questions MCQ Test Signals and Systems - Test: Backward Difference Method

Test: Backward Difference Method for Electronics and Communication Engineering (ECE) 2024 is part of Signals and Systems preparation. The Test: Backward Difference Method questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Backward Difference Method MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Backward Difference Method below.
Solutions of Test: Backward Difference Method questions in English are available as part of our Signals and Systems for Electronics and Communication Engineering (ECE) & Test: Backward Difference Method solutions in Hindi for Signals and Systems course. Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free. Attempt Test: Backward Difference Method | 10 questions in 10 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study Signals and Systems for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
Test: Backward Difference Method - Question 1
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The equation for Heq(s) is

Detailed Solution for Test: Backward Difference Method - Question 1

Explanation: The analog filter in the time domain is governed by the following difference equation,

Test: Backward Difference Method - Question 2
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 What is the first backward difference of y(n)?

Detailed Solution for Test: Backward Difference Method - Question 2

Explanation: A simple approximation to the first order derivative is given by the first backward difference. The first backward difference is defined by
[y(n)-y(n-1)]/T.

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Test: Backward Difference Method - Question 3
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 Which of the following is the correct relation between ‘s’ and ‘z’?

Detailed Solution for Test: Backward Difference Method - Question 3

Explanation: We know that s=(1-z-1)/T=> z=1/(1-sT).

Test: Backward Difference Method - Question 4
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What is the center of the circle represented by the image of jΩ axis of the s-domain?
Detailed Solution for Test: Backward Difference Method - Question 4

Explanation: Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get
|z-0.5|=0.5
Thus the image of the jΩ axis of the s-domain is a circle with centre at z=0.5 in z-domain

Test: Backward Difference Method - Question 5
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 What is the radius of the circle represented by the image of jΩ axis of the s-domain?
Detailed Solution for Test: Backward Difference Method - Question 5

Explanation: Letting s=σ+jΩ in the equation z=1/(1-sT) and by letting σ=0, we get
|z-0.5|=0.5
Thus the image of the jΩ axis of the s-domain is a circle of radius 0.5 centered at z=0.5 in z-domain.

Test: Backward Difference Method - Question 6
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 The frequency response H(ω) will be considerably distorted with respect to H(jΩ).
Detailed Solution for Test: Backward Difference Method - Question 6

Explanation: Since jΩ axis is not mapped to the circle |z|=1, we can expect that the frequency response H(ω) will be considerably distorted with respect to H(jΩ).

Test: Backward Difference Method - Question 7
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 The left half of the s-plane is mapped to which of the following in the z-domain?
Detailed Solution for Test: Backward Difference Method - Question 7

Explanation: The left half of the s-plane is mapped inside the circle of |z-0.5|=0.5 in the z-plane, which completely lies in the right half z-plane.

Test: Backward Difference Method - Question 8
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 An analog high pass filter can be mapped to a digital high pass filter.
Detailed Solution for Test: Backward Difference Method - Question 8

Explanation: An analog high pass filter cannot be mapped to a digital high pass filter because the poles of the digital filter cannot lie in the correct region, which is the left-half of the z-plane(z < 0) in this case.

Test: Backward Difference Method - Question 9
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Which of the following is the correct relation between ‘s’ and ‘z’? 
Detailed Solution for Test: Backward Difference Method - Question 9

Explanation: We know that z=1/(1-sT)=> s=(1-z-1)/T.

Test: Backward Difference Method - Question 10
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What is the z-transform of the first backward difference equation of y(n)? 
Detailed Solution for Test: Backward Difference Method - Question 10

 

Explanation: The first backward difference of y(n) is given by the equation
[y(n)-y(n-1)]/T
Thus the z-transform of the first backward difference of y(n) is given as

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