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 K_{P}?

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 K_{S}?**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 K_{P} and K_{S}?

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 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) 4**b) 5**

c) 6

d) 3

11. 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**

12. 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) 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?

a) 2 rad/sec

b) 2.25 Hz**c) 2.25 rad/sec**

d) 2 Hz

19. 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

20. Which of the following condition is true?

a) N ≤ log(1k)log(1d)

b) N ≤ log(k)log(d)

c) N ≤ log(d)log(k)**d) N ≤ log(1d)log(1k)**