1. Which of the following defines a Chebyshev polynomial of order N, T_{N}(x)?

A. cos(Ncos^{-1}x) for all x

B. cosh(Ncosh^{-1}x) for all x

C.cos(Ncos^{-1}x), |x|-1x), |x|>1

D. None of the mentioned

2. What is the formula for chebyshev polynomial T_{N}(x) in recursive form?

A. 2T_{N-1}(x) – T_{N-2}(x)

B. 2T_{N-1}(x) + T_{N-2}(x)

C. 2xT_{N-1}(x) + T_{N-2}(x)

D. 2xT_{N-1}(x) – T_{N-2}(x)

3. What is the value of the Chebyshev polynomial of degree 0?

A. 1

B. 0

C. -1

D. 2

4. What is the value of the 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. 3x^{3}+4x

B. 3x^{3}-4x

C. 4x^{3}+3x

D. 4x^{3}-3x

6. What is the value of Chebyshev polynomial of degree 5?

A. 16x^{5}+20x^{3}-5x

B. 16x^{5}+20x^{3}+5x

C. 16x^{5}-20x^{3}+5x

D. 16x^{5}-20x^{3}-5x

7. For |x|≤1, |T_{N}(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 T_{N}(0) for even degree N?

A. -1

B. +1

C. 0

D. ±1

10. T_{N}(-x)=(-1)^{N}T_{N}(x).

A. True

B. False

11. What is the value of |T_{N}(±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 N_{B} and N_{C} 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 the passband and monotonic in the stopband.

A. True

B. False

15. What is the equation for magnitude frequency response |H(jΩ)| of a low pass chebyshev-I filter?

A. \(\frac{1}{\sqrt{1-ϵ T_N^2 (\frac{Ω}{Ω_P})}}\)

B. \(\frac{1}{\sqrt{1+ϵ T_N^2 (\frac{Ω}{Ω_P})}}\)

C. \(\frac{1}{\sqrt{1-ϵ^2 T_N^2 (\frac{Ω}{Ω_P})}}\)

D. \(\frac{1}{\sqrt{1+ϵ^2 T_N^2 (\frac{Ω}{Ω_P})}}\)

16. What is the number of minima present in the passband of the 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 passband of the 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 the number of maxima and minima in the passband 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+ϵ^{2}T_{N}^{2}(s/j)=0

B. 1-ϵ^{2}T_{N}^{2}(s/j)=0

C. 1+ϵ T_{N}^{2}(s/j)=0

D. None of the mentioned

20. The poles of H_{N}(s).H_{N}(-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

22. The equation for H<sub>eq</sub>(s) is \(\frac{\sum_{K=0}^M b_K s^K}{\sum_{K=0}^N a_K s^K}\)

A. True

B. False

23. What is the first backward difference of y(n)?

A. [y(n)+y(n-1)]/T

B. [y(n)+y(n+1)]/T

C. [y(n)-y(n+1)]/T

D. [y(n)-y(n-1)]/T

24. Which of the following is the correct relation between ‘s’ and ‘z’?

A. z=1/(1+sT)

B. s=1/(1+zT)

C. z=1/(1-sT)

D. none of the mentioned

25. What is the center of the circle represented by the image of jΩ axis of the s-domain?

A. z=0

B. z=0.5

C. z=1

D. none of the mentioned