# 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 KP=-1 dB at ΩP=4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS=8 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 KP=-1 dB at ΩP=4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS=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?
b) 2.25 Hz
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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