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