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Test: Backward Difference Method


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

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

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

 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.

Test: Backward Difference Method - Question 3

 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

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

 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

 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

 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

 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

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

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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