Bilinear Transformations

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Bilinear Transformations”.

1. Bilinear Transformation is used for transforming an analog filter to a digital filter.
a) True
b) False

2. Which of the following rule is used in the bilinear transformation?
a) Simpson’s rule
b) Backward difference
c) Forward difference
d) Trapezoidal rule

3. Which of the following substitution is done in Bilinear transformations?
a) s = 2T[1+z−11−z1]
b) s = 2T[1+z−11+]
c) s = 2T[1−z−11+z−1]
d) None of the mentioned

4. What is the value of ∫nT(n−1)Tx(t)dt according to trapezoidal rule?
a) [x(nT)−x[(n−1)T]2]T
b) [x(nT)+x[(n−1)T]2]T
c) [x(nT)−x[(n+1)T]2]T
d) [x(nT)+x[(n+1)T]2]T

5. What is the value of y(n)-y(n-1) in terms of input x(n)?
a) [x(n)+x(n−1)2]T
b) [x(n)−x(n−1)2]T
c) [x(n)−x(n+1)2]T
d) [x(n)+x(n+1)2]T

6. What is the expression for system function in z-domain?
a) 2T[1+z−11−z1]
b) 2T[1+z−11−z1]
c) T2[1+z−11−z1]
d) T2[1−z−11+z−1]

7. In bilinear transformation, the left-half s-plane is mapped to which of the following in the z-domain?
a) Entirely outside the unit circle |z|=1
b) Partially outside the unit circle |z|=1
c) Partially inside the unit circle |z|=1
d) Entirely inside the unit circle |z|=1

8. The equation s = 2T[1−z−11+z−1] is a true frequency-to-frequency transformation.
a) True
b) False

9. If s=σ+jΩ and z=re, then what is the condition on σ if r<1?
a) σ > 0
b) σ < 0
c) σ > 1
d) σ < 1

10. If s=σ+jΩ and z=re and r=1, then which of the following inference is correct?
a) LHS of the s-plane is mapped inside the circle, |z|=1
b) RHS of the s-plane is mapped outside the circle, |z|=1
c) Imaginary axis in the s-plane is mapped to the circle, |z|=1
d) None of the mentioned

11. If s=σ+jΩ and z=re, then what is the condition on σ if r>1?
a) σ > 0
b) σ < 0
c) σ > 1
d) σ < 1

12. What is the expression for the digital frequency when r=1?
a) 1Ttan(ΩT2)
b) 2Ttan(ΩT2)
c) 1Ttan−1(ΩT2)
d) 2Ttan−1(ΩT2)

13. What is the kind of relationship between Ω and ω?
a) Many-to-one
b) One-to-many
c) One-to-one
d) Many-to-many

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