1. Which of the following is true in the case of Butterworth filters?

A. Smooth passband

B. Wide transition band

C. Not so smooth stopband

D. All of the mentioned

2. What is the magnitude frequency response of a Butterworth filter of order N and cutoff frequency ΩC?

A. \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

B. \(1+(\frac{Ω}{Ω_C})^{2N}\)

C. \(\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}\)

D. None of the mentioned

3. What is the factor to be multiplied to the dc gain of the filter to obtain filter magnitude at cutoff frequency?

A. 1

B. √2

C. 1/√2

D. 1/2

4. What is the value of magnitude frequency response of a Butterworth low pass filter at Ω=0?

A. 0

B. 1

C. 1/√2

D. None of the mentioned

5. As the value of the frequency Ω tends to ∞, then |H(jΩ)| tends to ____________

A. 0

B. 1

C. ∞

D. None of the mentioned

6. |H(jΩ)| is a monotonically increasing function of frequency.

A. True

B. False

7. What is the magnitude squared response of the normalized low pass Butterworth filter?

A. \(\frac{1}{1+Ω^{-2N}}\)

B. 1+Ω-2N

C. 1+Ω2N

D. \(\frac{1}{1+Ω^{2N}}\)

8. What is the transfer function of magnitude squared frequency response of the normalized low pass Butterworth filter?

A. \(\frac{1}{1+(s/j)^{2N}}\)

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

C. \(1+(\frac{s}{j})^{2N}\)

D. \(\frac{1}{1+(s/j)^{-2N}}\)

9. Where does the poles of the transfer function of normalized low pass Butterworth filter exists?

A. Inside unit circle

B. Outside unit circle

C. On unit circle

D. None of the mentioned

10. What is the general formula that represents the phase of the poles of the transfer function of normalized low pass Butterworth filter of order N?

A. \(\frac{π}{N} k+\frac{π}{2N}\) k=0,1,2…N-1

B. \(\frac{π}{N} k+\frac{π}{2N}+\frac{π}{2}\) k=0,1,2…2N-1

C. \(\frac{π}{N} k+\frac{π}{2N}+\frac{π}{2}\) k=0,1,2…N-1

D. \(\frac{π}{N} k+\frac{π}{2N}\) k=0,1,2…2N-1

11. What is the Butterworth polynomial of order 3?

A. (s2+s+1)(s-1)

B. (s2-s+1)(s-1)

C. (s2-s+1)(s+1)

D. (s2+s+1)(s+1)

12. What is the Butterworth polynomial of order 1?

A. s-1

B. s+1

C. s

D. none of the mentioned

13. What is the transfer function of Butterworth low pass filter of order 2?

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

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

C. \(s^2-\sqrt{2} s+1\)

D. \(s^2+\sqrt{2} s+1\)

14. What is the passband edge frequency of an analog low pass normalized filter?

A. 0 rad/sec

B. 0.5 rad/sec

C. 1 rad/sec

D. 1.5 rad/sec

15. If H(s) is the transfer function of an analog low pass normalized filter and Ωu is the desired passband edge frequency of the new low pass filter, then which of the following transformation has to be performed?

A. s → s/Ωu

B. s → s.Ωu

C. s → Ωu/s

D. none of the mentioned

16. Which of the following is a low pass-to-high pass transformation?

A. s → s / Ωu

B. s → Ωu / s

C. s → Ωu.s

D. none of the mentioned

17. Which of the following is the backward design equation for a low pass-to-low pass transformation?

A. \(\Omega_S=\frac{\Omega_S}{\Omega_u}\)

B. \(\Omega_S=\frac{\Omega_u}{\Omega’_S}\)

C. \(\Omega’_S=\frac{\Omega_S}{\Omega_u}\)

D. \(\Omega_S=\frac{\Omega’_S}{\Omega_u}\)

18. Which of the following is a low pass-to-band pass transformation?

A. s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u+Ω_l)}\)

B. s→\(\frac{s^2-Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

C. s→\(\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}\)

D. s→\(\frac{s^2-Ω_u Ω_l}{s(Ω_u+Ω_l)}\)

19. Which of the following is the backward design equation for a low pass-to-high pass transformation?

A. \(\Omega_S=\frac{\Omega_S}{\Omega_u}\)

B. \(\Omega_S=\frac{\Omega_u}{\Omega’_S}\)

C. \(\Omega’_S=\frac{\Omega_S}{\Omega_u}\)

D. \(\Omega_S=\frac{\Omega’_S}{\Omega_u}\)

20. Which of the following is a low pass-to-band stop transformation?

A. s→\(\frac{s(Ω_u-Ω_l)}{s^2+Ω_u Ω_l}\)

B. s→\(\frac{s(Ω_u+Ω_l)}{s^2+Ω_u Ω_l}\)

C. s→\(\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}\)

D. none of the mentioned

21. If A=\(\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}\) and B=\(\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}\), then which of the following is the backward design equation for a low pass-to-band pass transformation?

A. ΩS=|B|

B. ΩS=|A|

C. ΩS=Max{|A|,|B|}

D. ΩS=Min{|A|,|B|}

22. If A=\(\frac{Ω_1 (Ω_u-Ω_l)}{-Ω_1^2+Ω_u Ω_l}\) and B=\(\frac{Ω_2 (Ω_u-Ω_l)}{Ω_2^2-Ω_u Ω_l}\), then which of the following is the backward design equation for a low pass-to-band stop transformation?

A. ΩS=Max{|A|,|B|}

B. ΩS=Min{|A|,|B|}

C. ΩS=|B|

D. ΩS=|A|

23. Which of the following is a low pass-to-high pass transformation?

A. s → s / Ωu

B. s → Ωu/s

C. s → Ωu.s

D. none of the mentioned

24. Which of the following operation has to be performed to increase the sampling rate by an integer factor I?

A. Interpolating I+1 new samples

B. Interpolating I-1 new samples

C. Extrapolating I+1 new samples

D. Extrapolating I-1 new samples