1. What is the region between origin and the passband frequency in the magnitude frequency response of a low pass filter?

A. Stopband

B. Passband

C. Transition band

D. None of the mentioned

2. What is the region between stopband and the passband frequencies in the magnitude frequency response of a low pass filter?

A. Stopband

B. Passband

C. Transition band

D. None of the mentioned

3. What is the region after the stopband frequency in the magnitude frequency response of a low pass filter?

A. Stopband

B. Passband

C. Transition band

D. None of the mentioned

4. If δP is the forbidden magnitude value in the passband and δS is the forbidden magnitude value in the stopband, then which of the following is true in the passband region?

A. 1-δS≤|H(jΩ)|≤1

B. δP≤|H(jΩ)|≤1

C. 0≤|H(jΩ)|≤ δS

D. 1-δP≤|H(jΩ)|≤1

5. If δP is the forbidden magnitude value in the passband and δS is the forbidden magnitude value in the stopband, then which of the following is true in the stopband region?

A. 1- δP≤|H(jΩ)|≤1

B. δP≤|H(jΩ)|≤1

C. 0≤|H(jΩ)|≤ δS

D. 1- δP≤|H(jΩ)|≤1

6. What is the value of passband ripple in dB?

A. -20log(1- δP)

B. -20log(δP)

C. 20log(1- δP)

D. None of the mentioned

7. What is the value of stopband ripple in dB?

A. -20log(1-δS)

B. -20log(δS)

C. 20log(1-δS)

D. None of the mentioned

8. What is the passband gain of a low pass filter with 1- δP as the passband attenuation?

A. -20log(1- δP)

B. -20log(δP)

C. 20log(δP)

D. 20log(1- δP)

9. What is the stopband gain of a low pass filter with δS as the passband attenuation?

A. -20log(1- δS)

B. -20log(δS)

C. 20log(δS)

D. 20log(1- δS)

10. What is the cutoff frequency of a normalized filter?

A. 2 rad/sec

B. 1 rad/sec

C. 0.5 rad/sec

D. None of the mentioned

11. The low pass, high pass, bandpass, and bandstop filters can be designed by applying a specific transformation to a normalized low pass filter.

A. True

B. False

12. 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

12. 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

13. 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

14. 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

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

A. 0

B. 1

C. ∞

D. None of the mentioned

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

A. True

B. False

17. 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. \(\frac{1}{1+Ω^{2N}}\)

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

19. Where do 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

20. 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

21. 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)

22. What is the Butterworth polynomial of order 1?

A. s-1

B. s+1

C. s

D. none of the mentioned

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