# Butterworth Filters Design

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Design of Low Pass Butterworth Filters-1”.

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−(ΩPΩC)2N]
b) -10 log[1+(ΩPΩC)2N]
c) 10 log[1−(ΩPΩC)2N]
d) 10 log[1+(ΩPΩC)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+(ΩSΩC)2N]
b) -10 log[1−(ΩSΩC)2N]
c) 10 log[1−(ΩSΩC)2N]
d) 10 log[1+(ΩSΩC)2N]

4. Which of the following equation is True?
a) [ΩPΩC]2N=10−KP/10+1
b) [ΩPΩC]2N=10KP/10+1
c) [ΩPΩC]2N=10−KP/10−1
d) None of the mentioned

5. Which of the following equation is True?
a) [ΩSΩC]2N=10−KS/10+1
b) [ΩSΩC]2N=10KS/10+1
c) [ΩSΩC]2N=10−KS/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) log[(10KP10−1)/(10Ks10−1)]2log(ΩPΩS)
b) log[(10KP10+1)/(10Ks10+1)]2log(ΩPΩS)
c) log[(10−KP10+1)/(10−Ks10+1)]2log(ΩPΩS)
d) log[(10−KP10−1)/(10−Ks10−1)]2log(ΩPΩS)

7. What is the expression for cutoff frequency in terms of pass band gain?
a) ΩP(10−KP/10−1)1/2N
b) ΩP(10−KP/10+1)1/2N
c) ΩP(10KP/10−1)1/2N
d) None of the mentioned

8. What is the expression for cutoff frequency in terms of stop band gain?
a) ΩS(10−KS/10−1)1/2N
b) ΩS(10−KS/10+1)1/2N
c) ΩS(10KS/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 pass band gain KP=-1 dB at ΩP=4 rad/sec and stop band 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 pass band gain KP=-1 dB at ΩP=4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS=8 rad/sec?

12. What is the system function of the Butterworth filter with specifications as pass band gain KP=-1 dB at ΩP=4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS=8 rad/sec?
a) 1s5+14.82s4+109.8s3+502.6s2+1422.3s+2012.4
b) 1s5+14.82s4+109.8s3+502.6s2+1422.3s+1
c) 2012.4s5+14.82s4+109.8s3+502.6s2+1422.3s+2012.4
d) None of the mentioned

13. If H(s)=1s2+s+1 represent the transfer function of a low pass filter (not Butterworth) with a pass band of 1 rad/sec, then what is the system function of a low pass filter with a pass band 10 rad/sec?
a) 100s2+10s+100
b) s2s2+s+1
c) s2s2+10s+100
d) None of the mentioned

14. If H(s)=1s2+s+1 represent the transfer function of a low pass filter (not Butterworth) with a pass band of 1 rad/sec, then what is the system function of a high pass filter with a cutoff frequency of 1rad/sec?
a) 100s2+10s+100
b) s2s2+s+1
c) s2s2+10s+100
d) None of the mentioned

15. If H(s)=1s2+s+1 represent the transfer function of a low pass filter (not Butterworth) with a pass band of 1 rad/sec, then what is the system function of a high pass filter with a cutoff frequency of 10 rad/sec?
a) 100s2+10s+100
b) s2s2+s+1
c) s2s2+10s+100
d) None of the mentioned

16. If H(s)=1s2+s+1 represent the transfer function of a low pass filter (not Butterworth) with a pass band of 1 rad/sec, then what is the system function of a band pass filter with a pass band of 10 rad/sec and a center frequency of 100 rad/sec?
a) s2s4+10s3+20100s2+105s+1
b) 100s2s4+10s3+20100s2+105s+1
c) s2s4+10s3+20100s2+105s+108
d) 100s2s4+10s3+20100s2+105s+108

17. If H(s)=1s2+s+1 represent the transfer function of a low pass filter (not Butterworth) with a pass band 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) (s2+100)2s4+2s3+204s2+200s+104
b) (s2+10)2s4+2s3+204s2+200s+104
c) (s2+10)2s4+2s3+400s2+200s+104
d) None of the mentioned

18. What is the stop band frequency of the normalized low pass Butterworth filter used to design a analog band pass filter with -3.0103dB upper and lower cutoff frequency of 50Hz and 20KHz and a stop band attenuation 20dB at 20Hz and 45KHz?
b) 2.25 Hz