1. Which of the following is a frequency domain specification?

A. 0 ≥ 20 log|H(jΩ)|

B. 20 log|H(jΩ)| ≥ KP

C. 20 log|H(jΩ)| ≤ KS

D. All of the mentioned

2. What is the value of gain at the pass band frequency, i.e., what is the value of KP?

A. -10 \(log [1-(\frac{\Omega_P}{\Omega_C})^{2N}]\)

B. -10 \(log [1+(\frac{\Omega_P}{\Omega_C})^{2N}]\)

C. 10 \(log [1-(\frac{\Omega_P}{\Omega_C})^{2N}]\)

D. 10 \(log [1+(\frac{\Omega_P}{\Omega_C})^{2N}]\)

3. What is the value of gain at the stop band frequency, i.e., what is the value of KS?

A. -10 \(log[1+(\frac{\Omega_S}{\Omega_C})^{2N}]\)

B. -10 \(log[1-(\frac{\Omega_S}{\Omega_C})^{2N}]\)

C. 10 \(log[1-(\frac{\Omega_S}{\Omega_C})^{2N}]\)

D. 10 \(log[1+(\frac{\Omega_S}{\Omega_C})^{2N}]\)

4. Which of the following equation is True?

A. \([\frac{\Omega_P}{\Omega_C}]^{2N} = 10^{-K_P/10}+1\)

B. \([\frac{\Omega_P}{\Omega_C}]^{2N} = 10^{K_P/10}+1\)

C. \([\frac{\Omega_P}{\Omega_C}]^{2N} = 10^{-K_P/10}-1\)

D. None of the mentioned

5. Which of the following equation is True?

A. \([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}+1\)

B. \([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{K_S/10}+1\)

C. \([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}-1\)

D. None of the mentioned

6. What is the order N of the low pass Butterworth filter in terms of KP and KS?

A. \(\frac{log[(10^\frac{K_P}{10}-1)/(10^\frac{K_s}{10}-1)]}{2 log(\frac{\Omega_P}{\Omega_S})}\)

B. \(\frac{log[(10^\frac{K_P}{10}+1)/(10^\frac{K_s}{10}+1)]}{2 log(\frac{\Omega_P}{\Omega_S})}\)

C. \(\frac{log[(10^\frac{-K_P}{10}+1)/(10^\frac{-K_s}{10}+1)]}{2 log(\frac{\Omega_P}{\Omega_S})}\)

D. \(\frac{log[(10^\frac{-K_P}{10}-1)/(10^\frac{-K_s}{10}-1)]}{2 log(\frac{\Omega_P}{\Omega_S})}\)

7. What is the expression for cutoff frequency in terms of passband gain?

A. \(\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}\)

B. \(\frac{\Omega_P}{(10^{-K_P/10}+1)^{1/2N}}\)

C. \(\frac{\Omega_P}{(10^{K_P/10}-1)^{1/2N}}\)

D. None of the mentioned

8. What is the expression for cutoff frequency in terms of stopband gain?

A. \(\frac{\Omega_S}{(10^{-K_S/10}-1)^{1/2N}}\)

B. \(\frac{\Omega_S}{(10^{-K_S/10}+1)^{1/2N}}\)

C. \(\frac{\Omega_S}{(10^{K_S/10}-1)^{1/2N}}\)

D. None of the mentioned

9. The cutoff frequency of the low pass Butterworth filter is the arithmetic mean of the two cutoff frequencies as found above.

A. True

B. False

10. What is the lowest order of the Butterworth filter with a passband gain KP=-1 dB at ΩP=4 rad/sec and stopband attenuation greater than or equal to 20dB at ΩS = 8 rad/sec?

A. 4

B. 5

C. 6

D. 3

11. What is the cutoff frequency of the Butterworth filter with a passband gain KP=-1 dB at ΩP=4 rad/sec and stopband attenuation greater than or equal to 20dB at ΩS=8 rad/sec?

A. 3.5787 rad/sec

B. 1.069 rad/sec

C. 6 rad/sec

D. 4.5787 rad/sec

12. What is the system function of the Butterworth filter with specifications as passband gain KP=-1 dB at ΩP=4 rad/sec and stopband attenuation greater than or equal to 20dB at ΩS=8 rad/sec?

A. \(\frac{1}{s^5+14.82s^4+109.8s^3+502.6s^2+1422.3s+2012.4}\)

B. \(\frac{1}{s^5+14.82s^4+109.8s^3+502.6s^2+1422.3s+1}\)

C. \(\frac{2012.4}{s^5+14.82s^4+109.8s^3+502.6s^2+1422.3s+2012.4}\)

D. None of the mentioned

13. If H(s)=\(\frac{1}{s^2+s+1}\) represents the transfer function of a low pass filter (not Butterworth) with a passband of 1 rad/sec, then what is the system function of a low pass filter with a passband 10 rad/sec?

A. \(\frac{100}{s^2+10s+100}\)

B. \(\frac{s^2}{s^2+s+1}\)

C. \(\frac{s^2}{s^2+10s+100}\)

D. None of the mentioned

14. If H(s)=\(\frac{1}{s^2+s+1}\) represents the transfer function of a low pass filter (not Butterworth) with a passband of 1 rad/sec, then what is the system function of a high pass filter with a cutoff frequency of 1rad/sec?

A. \(\frac{100}{s^2+10s+100}\)

B. \(\frac{s^2}{s^2+s+1}\)

C. \(\frac{s^2}{s^2+10s+100}\)

D. None of the mentioned

15. If H(s)=\(\frac{1}{s^2+s+1}\) represents the transfer function of a low pass filter (not Butterworth) with a passband of 1 rad/sec, then what is the system function of a high pass filter with a cutoff frequency of 10 rad/sec?

A. \(\frac{100}{s^2+10s+100}\)

B. \(\frac{s^2}{s^2+s+1}\)

C. \(\frac{s^2}{s^2+10s+100}\)

D. None of the mentioned

16. If H(s)=\(\frac{1}{s^2+s+1}\) represents the transfer function of a low pass filter (not Butterworth) with a passband of 1 rad/sec, then what is the system function of a bandpass filter with a passband of 10 rad/sec and a center frequency of 100 rad/sec?

A. \(\frac{s^2}{s^4+10s^3+20100s^2+10^5 s+1}\)

B. \(\frac{100s^2}{s^4+10s^3+20100s^2+10^5 s+1}\)

C. \(\frac{s^2}{s^4+10s^3+20100s^2+10^5 s+10^8}\)

D. \(\frac{100s^2}{s^4+10s^3+20100s^2+10^5 s+10^8}\)

17. If H(s)=\(\frac{1}{s^2+s+1}\) represents the transfer function of a low pass filter (not Butterworth) with a passband of 1 rad/sec, then what is the system function of a stop band filter with a stop band of 2 rad/sec and a center frequency of 10 rad/sec?

A. \(\frac{(s^2+100)^2}{s^4+2s^3+204s^2+200s+10^4}\)

B. \(\frac{(s^2+10)^2}{s^4+2s^3+204s^2+200s+10^4}\)

C. \(\frac{(s^2+10)^2}{s^4+2s^3+400s^2+200s+10^4}\)

D. None of the mentioned

18. What is the stopband frequency of the normalized low pass Butterworth filter used to design an analog bandpass filter with -3.0103dB upper and lower cutoff frequency of 50Hz and 20KHz and a stopband attenuation 20dB at 20Hz and 45KHz?

A. 2 rad/sec

B. 2.25 Hz

C. 2.25 rad/sec

D. 2 Hz

19. What is the order of the normalized low pass Butterworth filter used to design an analog bandpass filter with -3.0103dB upper and lower cutoff frequency of 50Hz and 20KHz and a stopband attenuation of 20dB at 20Hz and 45KHz?

A. 2

B. 3

C. 4

D. 5

20. Which of the following condition is true?

A. N ≤ \(\frac{log(\frac{1}{k})}{log(\frac{1}{d})}\)

B. N ≤ \(\frac{log(k)}{log(D.}\)

C. N ≤ \(\frac{log(D.}{log(k)}\)

D. N ≤ \(\frac{log(\frac{1}{d})}{log(\frac{1}{k})}\)

21. 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

22. 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)

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

A. 1

B. 0

C. -1

D. 2

24. What is the value of the Chebyshev polynomial of degree 1?

A. 1

B. x

C. -1

D. -x

25. 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