# Butterworth Filters Design 1 MCQ’s

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

1. What is the expression for cutoff frequency in terms of pass band gain?
a) $$\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}$$
b) $$\frac{\Omega_P}{(10^{-K_P/10}+1)^{1/2N}}$$
c) $$\frac{\Omega_P}{(10^{K_P/10}-1)^{1/2N}}$$
d) None 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 $$log⁡ [1-(\frac{\Omega_P}{\Omega_C})^{2N}]$$
b) -10 $$log⁡ [1+(\frac{\Omega_P}{\Omega_C})^{2N}]$$
c) 10 $$log⁡ [1-(\frac{\Omega_P}{\Omega_C})^{2N}]$$
d) 10 $$log⁡ [1+(\frac{\Omega_P}{\Omega_C})^{2N}]$$

3. 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

4. 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

5. Which of the following equation is True?
a) $$[\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}+1$$
b) $$[\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{K_S/10}+1$$
c) $$[\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}-1$$
d) None of the mentioned

6. 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

7. What is the order N of the low pass Butterworth filter in terms of KP and KS?
a) $$\frac{log⁡[(10^\frac{K_P}{10}-1)/(10^\frac{K_s}{10}-1)]}{2 log⁡(\frac{\Omega_P}{\Omega_S})}$$
b) $$\frac{log⁡[(10^\frac{K_P}{10}+1)/(10^\frac{K_s}{10}+1)]}{2 log⁡(\frac{\Omega_P}{\Omega_S})}$$
c) $$\frac{log⁡[(10^\frac{-K_P}{10}+1)/(10^\frac{-K_s}{10}+1)]}{2 log⁡(\frac{\Omega_P}{\Omega_S})}$$
d) $$\frac{log⁡[(10^\frac{-K_P}{10}-1)/(10^\frac{-K_s}{10}-1)]}{2 log⁡(\frac{\Omega_P}{\Omega_S})}$$

8. Which of the following equation is True?
a) $$[\frac{\Omega_P}{\Omega_C}]^{2N} = 10^{-K_P/10}+1$$
b) $$[\frac{\Omega_P}{\Omega_C}]^{2N} = 10^{K_P/10}+1$$
c) $$[\frac{\Omega_P}{\Omega_C}]^{2N} = 10^{-K_P/10}-1$$
d) None of the mentioned

9. What is the expression for cutoff frequency in terms of stop band gain?
a) $$\frac{\Omega_S}{(10^{-K_S/10}-1)^{1/2N}}$$
b) $$\frac{\Omega_S}{(10^{-K_S/10}+1)^{1/2N}}$$
c) $$\frac{\Omega_S}{(10^{K_S/10}-1)^{1/2N}}$$
d) None of the mentioned

10. What is the value of gain at the stop band frequency, i.e., what is the value of KS?
a) -10 $$log⁡[1+(\frac{\Omega_S}{\Omega_C})^{2N}]$$
b) -10 $$log⁡[1-(\frac{\Omega_S}{\Omega_C})^{2N}]$$
c) 10 $$log⁡[1-(\frac{\Omega_S}{\Omega_C})^{2N}]$$
d) 10 $$log⁡[1+(\frac{\Omega_S}{\Omega_C})^{2N}]$$

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