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, 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|<1 cosh(Ncosh^{-1}x), |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 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) 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) N_{C}=N_{B}**b) N _{C}<N_{B}**

c) N

_{C}>N

_{B}

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+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