Chebyshev Filters

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Chebyshev Filters-1”.

1. Which of the following defines a chebyshev polynomial of order N, TN(x)?
a) cos(Ncos-1x) for all x
b) cosh(Ncosh-1x) for all x
c)

cos(Ncos-1x), |x|<1
cosh(Ncosh-1x), |x|>1

d) None of the mentioned

2. What is the formula for chebyshev polynomial TN(x) in recursive form?
a) 2TN-1(x) – TN-2(x)
b) 2TN-1(x) + TN-2(x)
c) 2xTN-1(x) + TN-2(x)
d) 2xTN-1(x) – TN-2(x)

3. What is the value of chebyshev polynomial of degree 0?
a) 1
b) 0
c) -1
d) 2

4. What is the value of chebyshev polynomial of degree 1?
a) 1
b) x
c) -1
d) -x

5. What is the value of chebyshev polynomial of degree 3?
a) 3x3+4x
b) 3x3-4x
c) 4x3+3x
d) 4x3-3x

6. What is the value of chebyshev polynomial of degree 5?
a) 16x5+20x3-5x
b) 16x5+20x3+5x
c) 16x5-20x3+5x
d) 16x5-20x3-5x

7. For |x|≤1, |TN(x)|≤1, and it oscillates between -1 and +1 a number of times proportional to N.
a) True
b) False

8. Chebyshev polynomials of odd orders are _____________
a) Even functions
b) Odd functions
c) Exponential functions
d) Logarithmic functions

9. What is the value of TN(0) for even degree N?
a) -1
b) +1
c) 0
d) ±1

10. TN(-x)=(-1)NTN(x).
a) True
b) False

11. What is the value of |TN(±1)|?
a) 0
b) -1
c) 1
d) None of the mentioned

12. The chebyshev polynomial is oscillatory in the range |x|<∞.
a) True
b) False

13. 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?
a) NC=NB
b) NC<NB
c) NC>NB
d) Cannot be determined

14. The chebyshev-I filter is equi-ripple in pass band and monotonic in the stop band.
a) True
b) False

15. What is the equation for magnitude frequency response |H(jΩ)| of a low pass chebyshev-I filter?
a) 11−ϵT2N(ΩΩP)√
b) 11+ϵT2N(ΩΩP)√
c) 11−ϵ2T2N(ΩΩP)√
d) 11+ϵ2T2N(ΩΩP)√

16. 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?
a) 1
b) 2
c) 3
d) 4

17. 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?
a) 1
b) 2
c) 3
d) 4

18. The sum of number of maxima and minima in the pass band equals the order of the filter.
a) True
b) False

19. Which of the following is the characteristic equation of a Chebyshev filter?
a) 1+ϵ2TN2(s/j)=0
b) 1-ϵ2TN2(s/j)=0
c) 1+ϵ TN2(s/j)=0
d) None of the mentioned

20. The poles of HN(s).HN(-s) are found to lie on ___________
a) Circle
b) Parabola
c) Hyperbola
d) Ellipse

21. 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?
a) 2
b) 5
c) 4
d) 3

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