# Butterworth Filters MCQ’s

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

1. What is the transfer function of magnitude squared frequency response of the normalized low pass Butterworth filter?
a) $$\frac{1}{1+(s/j)^{2N}}$$
b) $$1+(\frac{s}{j})^{-2N}$$
c) $$1+(\frac{s}{j})^{2N}$$
d) $$\frac{1}{1+(s/j)^{-2N}}$$

2. What is the general formula that represent the phase of the poles of transfer function of normalized low pass Butterworth filter of order N?
a) $$\frac{π}{N} k+\frac{π}{2N}$$ k=0,1,2…N-1
b) $$\frac{π}{N} k+\frac{π}{2N}+\frac{π}{2}$$ k=0,1,2…2N-1
c) $$\frac{π}{N} k+\frac{π}{2N}+\frac{π}{2}$$ k=0,1,2…N-1
d) $$\frac{π}{N} k+\frac{π}{2N}$$ k=0,1,2…2N-1

3. As the value of the frequency Ω tends to ∞, then |H(jΩ)| tends to ____________
a) 0
b) 1
c) ∞
d) None of the mentioned

4. What is the transfer function of Butterworth low pass filter of order 2?
a) $$\frac{1}{s^2+\sqrt{2} s+1}$$
b) $$\frac{1}{s^2-\sqrt{2} s+1}$$
c) $$s^2-\sqrt{2} s+1$$
d) $$s^2+\sqrt{2} s+1$$

5. What is the value of magnitude frequency response of a Butterworth low pass filter at Ω=0?
a) 0
b) 1
c) 1/√2
d) None of the mentioned

6. What is the magnitude squared response of the normalized low pass Butterworth filter?
a) $$\frac{1}{1+Ω^{-2N}}$$
b) 1+Ω-2N
c) 1+Ω2N
d) $$\frac{1}{1+Ω^{2N}}$$

7. |H(jΩ)| is a monotonically increasing function of frequency.
a) True
b) False

8. What is the factor to be multiplied to the dc gain of the filter to obtain filter magnitude at cutoff frequency?
a) 1
b) √2
c) 1/√2
d) 1/2

9. Which of the following is true in the case of Butterworth filters?
a) Smooth pass band
b) Wide transition band
c) Not so smooth stop band
d) All of the mentioned

10. Where does the poles of the transfer function of normalized low pass Butterworth filter exists?
a) Inside unit circle
b) Outside unit circle
c) On unit circle
d) None of the mentioned

11. What is the Butterworth polynomial of order 3?
a) (s2+s+1)(s-1)
b) (s2-s+1)(s-1)
c) (s2-s+1)(s+1)
d) (s2+s+1)(s+1)

12. What is the magnitude frequency response of a Butterworth filter of order N and cutoff frequency ΩC?
a) $$\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}$$
b) $$1+(\frac{Ω}{Ω_C})^{2N}$$
c) $$\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}$$
d) None of the mentioned

13. What is the Butterworth polynomial of order 1?
a) s-1
b) s+1
c) s
d) none of the mentioned