Digital Signal Processing

Butterworth Filters

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the magnitude frequency response of a Butterworth filter of order N and cutoff frequency ΩC?
\\(\\frac{1}{\\sqrt{1+(\\frac{Ω}{Ω_C})^{2N}}}\\)
\\(1+(\\frac{Ω}{Ω_C})^{2N}\\)
\\(\\sqrt{1+(\\frac{Ω}{Ω_C})^{2N}}\\)
None of the mentioned
Explanation:
A Butterworth is characterized by the magnitude frequency response
Question 2
Marks : +2 | -2
Pass Ratio : 100%
What is the transfer function of magnitude squared frequency response of the normalized low pass Butterworth filter?
\\(\\frac{1}{1+(s/j)^{2N}}\\)
\\(1+(\\frac{s}{j})^{-2N}\\)
\\(1+(\\frac{s}{j})^{2N}\\)
\\(\\frac{1}{1+(s/j)^{-2N}}\\)
Explanation:
We know that the magnitude squared frequency response of a normalized low pass Butterworth filter is given as
Question 3
Marks : +2 | -2
Pass Ratio : 100%
What is the factor to be multiplied to the dc gain of the filter to obtain filter magnitude at cutoff frequency?
1
√2
1/√2
1/2
Explanation:
The dc gain of the filter is the filter magnitude at Ω=0.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is true in the case of Butterworth filters?
Smooth pass band
Wide transition band
Not so smooth stop band
All of the mentioned
Explanation:
Butterworth filters have a very smooth pass band, which we pay for with a relatively wide transmission region.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the magnitude squared response of the normalized low pass Butterworth filter?
\\(\\frac{1}{1+Ω^{-2N}}\\)
1+Ω-2N
1+Ω2N
\\(\\frac{1}{1+Ω^{2N}}\\)
Explanation:
We know that the magnitude response of a low pass Butterworth filter of order N is given as
Question 6
Marks : +2 | -2
Pass Ratio : 100%
As the value of the frequency Ω tends to ∞, then |H(jΩ)| tends to ____________
0
1
∞
None of the mentioned
Explanation:
We know that the magnitude frequency response of a Butterworth filter of order N is given by the expression
Question 7
Marks : +2 | -2
Pass Ratio : 100%
Where does the poles of the transfer function of normalized low pass Butterworth filter exists?
Inside unit circle
Outside unit circle
On unit circle
None of the mentioned
Explanation:
The transfer function of normalized low pass Butterworth filter is given as
Question 8
Marks : +2 | -2
Pass Ratio : 100%
|H(jΩ)| is a monotonically increasing function of frequency.
True
False
Explanation:
|H(jΩ)| is a monotonically decreasing function of frequency, i.e., |H(jΩ2)| < |H(jΩ1)| for any values of Ω1 and Ω2 such that 0 ≤ Ω1 < Ω2.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
What is the general formula that represent the phase of the poles of transfer function of normalized low pass Butterworth filter of order N?
\\(\\frac{Ï€}{N} k+\\frac{Ï€}{2N}\\) k=0,1,2…N-1
\\(\\frac{Ï€}{N} k+\\frac{Ï€}{2N}+\\frac{Ï€}{2}\\) k=0,1,2…2N-1
\\(\\frac{Ï€}{N} k+\\frac{Ï€}{2N}+\\frac{Ï€}{2}\\) k=0,1,2…N-1
\\(\\frac{Ï€}{N} k+\\frac{Ï€}{2N}\\) k=0,1,2…2N-1
Explanation:
The transfer function of normalized low pass Butterworth filter is given as
Question 10
Marks : +2 | -2
Pass Ratio : 100%
What is the value of magnitude frequency response of a Butterworth low pass filter at Ω=0?
0
1
1/√2
None of the mentioned
Explanation:
The magnitude frequency response of a Butterworth low pass filter is given as