11. If fl and fu are the cutoff frequencies, then what is the desired real-valued frequency response of a Hilbert transform filter in the frequency range 2π flu?
A. -1
B. -0.5
C. 0
D. 1
12. What is the value of unit sample response of an ideal Hilbert transform for ‘n’ even?
A. -1
B. 1
C. 0
D. None of the mentioned
13. 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
14. 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 \(log [1+(\frac{\Omega_P}{\Omega_C})^{2N}]\)
15. 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 \(log[1+(\frac{\Omega_S}{\Omega_C})^{2N}]\)
16. 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
17. 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
18. 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. \(\frac{log[(10^\frac{-K_P}{10}-1)/(10^\frac{-K_s}{10}-1)]}{2 log(\frac{\Omega_P}{\Omega_S})}\)
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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