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Test: Bilinear Transformations


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10 Questions MCQ Test Signals and Systems | Test: Bilinear Transformations

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

Bilinear Transformation is used for transforming an analog filter to a digital filter.

Detailed Solution for Test: Bilinear Transformations - Question 1

Explanation: The bilinear transformation can be regarded as a correction of the backward difference method. The bilinear transformation is used for transforming an analog filter to a digital filter.

Test: Bilinear Transformations - Question 2

 Which of the following rule is used in the bilinear transformation?

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Explanation: Bilinear transformation uses trapezoidal rule for integrating a continuous time function.

Test: Bilinear Transformations - Question 3

 Which of the following substitution is done in Bilinear transformations?

Detailed Solution for Test: Bilinear Transformations - Question 3

 

Explanation: In bilinear transformation of an analog filter to digital filter, using the trapezoidal rule, the substitution for ‘s’ is given as

Test: Bilinear Transformations - Question 4

 What is the value of according to trapezoidal rule?

Detailed Solution for Test: Bilinear Transformations - Question 4

Explanation: The given integral is approximated by the trapezoidal rule. This rule states that if T is small, the area (integral) can be approximated by the mean height of x(t) between the two limits and then multiplying by the width. That is

Test: Bilinear Transformations - Question 5

What is the value of y(n)-y(n-1) in terms of input x(n)?

Detailed Solution for Test: Bilinear Transformations - Question 5

Explanation: We know that the derivate equation is
dy(t)/dt=x(t)

Test: Bilinear Transformations - Question 6

What is the expression for system function in z-domain?

Detailed Solution for Test: Bilinear Transformations - Question 6

Explanation: We know that
y(n)-y(n-1)= [(x(n)+x(n-1))/2]T
Taking z-transform of the above equation gives
=>Y(z)[1-z-1]=([1+z-1]/2).TX(z)
=>H(z)=Y(z)/X(z)= T/2[(1+z-1)/(1-z1 )].

Test: Bilinear Transformations - Question 7

 In bilinear transformation, the left-half s-plane is mapped to which of the following in the z-domain?

Detailed Solution for Test: Bilinear Transformations - Question 7

Explanation: In bilinear transformation, the z to s transformation is given by the expression
z=[1+(T/2)s]/[1-(T/2)s].
Thus unlike the backward difference method, the left-half s-plane is now mapped entirely inside the unit circle, |z|=1, rather than to a part of it.

Test: Bilinear Transformations - Question 8

 The equationis a true frequency-to-frequency transformation. 

Detailed Solution for Test: Bilinear Transformations - Question 8

Explanation: Unlike the backward difference method, the left-half s-plane is now mapped entirely inside the unit circle, |z|=1, rather than to a part of it. Also, the imaginary axis is mapped to the unit circle. Therefore, equation is a true frequency-to-frequency transformation.

Test: Bilinear Transformations - Question 9

 If s=σ+jΩ and z=re, then what is the condition on σ if r<1? 

Detailed Solution for Test: Bilinear Transformations - Question 9

Explanation: We know that if =σ+jΩ and z=re, then by substituting the values in the below expression

When r<1 => σ < 0.

Test: Bilinear Transformations - Question 10

If s=σ+jΩ and z=re and r=1, then which of the following inference is correct? 

Detailed Solution for Test: Bilinear Transformations - Question 10

Explanation: We know that if =σ+jΩ and z=re, then by substituting the values in the below expression

=>σ = 2/T[(r2-1)/(r2+1+2rcosω)] When r=1 => σ = 0.
This shows that the imaginary axis in the s-domain is mapped to the circle of unit radius centered at z=0 in the z-domain.

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