# Butterworth Filters Design 2 MCQ’s

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

1. What is the order 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?

a) 2

b) 3

c) 4

d) 5

2. Which of the following condition is true?

a) N ≤ \(\frac{log(\frac{1}{k})}{log(\frac{1}{d})}\)

b) N ≤ \(\frac{log(k)}{log(d)}\)

c) N ≤ \(\frac{log(d)}{log(k)}\)

d) N ≤ \(\frac{log(\frac{1}{d})}{log(\frac{1}{k})}\)

3. What is the cutoff frequency of the Butterworth filter with a pass band gain K_{P}=-1 dB at Ω_{P}=4 rad/sec and stop band attenuation greater than or equal to 20dB at Ω_{S}=8 rad/sec?

a) 3.5787 rad/sec

b) 1.069 rad/sec

c) 6 rad/sec

d) 4.5787 rad/sec

4. If H(s)=\(\frac{1}{s^2+s+1}\) 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) \(\frac{100}{s^2+10s+100}\)

b) \(\frac{s^2}{s^2+s+1}\)

c) \(\frac{s^2}{s^2+10s+100}\)

d) None of the mentioned

5. If H(s)=\(\frac{1}{s^2+s+1}\) 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) \(\frac{s^2}{s^4+10s^3+20100s^2+10^5 s+1}\)

b) \(\frac{100s^2}{s^4+10s^3+20100s^2+10^5 s+1}\)

c) \(\frac{s^2}{s^4+10s^3+20100s^2+10^5 s+10^8}\)

d) \(\frac{100s^2}{s^4+10s^3+20100s^2+10^5 s+10^8}\)

6. What is the system function of the Butterworth filter with specifications as pass band gain K_{P}=-1 dB at Ω_{P}=4 rad/sec and stop band attenuation greater than or equal to 20dB at Ω_{S}=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

7. If H(s)=\(\frac{1}{s^2+s+1}\) 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) \(\frac{100}{s^2+10s+100}\)

b) \(\frac{s^2}{s^2+s+1}\)

c) \(\frac{s^2}{s^2+10s+100}\)

d) None of the mentioned

8. If H(s)=\(\frac{1}{s^2+s+1}\) represent 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

9. What is the stopband frequency of the normalized low pass Butterworth filter used to design an analog bandpass filter with -3.0103dB upper and lower cutoff frequency of 50Hz and 20KHz and a stopband attenuation 20dB at 20Hz and 45KHz?

a) 2 rad/sec

b) 2.25 Hz

c) 2.25 rad/sec

d) 2 Hz

10. If H(s)=\(\frac{1}{s^2+s+1}\) 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) \(\frac{(s^2+100)^2}{s^4+2s^3+204s^2+200s+10^4}\)

b) \(\frac{(s^2+10)^2}{s^4+2s^3+204s^2+200s+10^4}\)

c) \(\frac{(s^2+10)^2}{s^4+2s^3+400s^2+200s+10^4}\)

d) None of the mentioned

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