Digital Signal Processing

Chebyshev Filters

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the equation for magnitude frequency response |H(jΩ)| of a low pass chebyshev-I filter?
\\(\\frac{1}{\\sqrt{1-ϵ T_N^2 (\\frac{Ω}{Ω_P})}}\\)
\\(\\frac{1}{\\sqrt{1+ϵ T_N^2 (\\frac{Ω}{Ω_P})}}\\)
\\(\\frac{1}{\\sqrt{1-ϵ^2 T_N^2 (\\frac{Ω}{Ω_P})}}\\)
\\(\\frac{1}{\\sqrt{1+ϵ^2 T_N^2 (\\frac{Ω}{Ω_P})}}\\)
Explanation:
The magnitude frequency response of a low pass chebyshev-I filter is given by
Question 2
Marks : +2 | -2
Pass Ratio : 100%
The chebyshev polynomial is oscillatory in the range |x|<∞.
True
False
Explanation:
The chebyshev polynomial is oscillatory in the range |x|≤1 and monotonic outside it.
Question 3
Marks : +2 | -2
Pass Ratio : 100%
If NB and NC are the orders of the Butterworth and Chebyshev filters respectively to meet the same frequency specifications, then which of the following relation is true?
NC=NB
NC<NB
NC>NB
Cannot be determined
Explanation:
The equi-ripple property of the chebyshev filter yields a narrower transition band compared with that obtained when the magnitude response is monotone. As a consequence of this, the order of a chebyshev filter needed to achieve the given frequency domain specifications is usually lower than that of a Butterworth filter.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
What is the value of |TN(±1)|?
0
-1
1
None of the mentioned
Explanation:
We know that a chebyshev polynomial of degree N is defined as
Question 5
Marks : +2 | -2
Pass Ratio : 100%
The sum of number of maxima and minima in the pass band equals the order of the filter.
True
False
Explanation:
In the pass band of the frequency response of the low pass chebyshev-I filter, the sum of number of maxima and minima is equal to the order of the filter.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
What is the number of minima’s present in the pass band of magnitude frequency response of a low pass chebyshev-I filter of order 4?
1
2
3
4
Explanation:
In the magnitude frequency response of a low pass chebyshev-I filter, the pass band has 2 maxima and 2 minima(order 4=2 maxima+2 minima).
Question 7
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the characteristic equation of a Chebyshev filter?
1+ϵ2TN2(s/j)=0
1-ϵ2TN2(s/j)=0
1+ϵ TN2(s/j)=0
None of the mentioned
Explanation:
We know that for a chebyshev filter, we have
Question 8
Marks : +2 | -2
Pass Ratio : 100%
The chebyshev-I filter is equi-ripple in pass band and monotonic in the stop band.
True
False
Explanation:
There are two types of chebyshev filters. The Chebyshev-I filter is equi-ripple in the pass band and monotonic in the stop band and the chebyshev-II filter is quite opposite.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The poles of HN(s).HN(-s) are found to lie on ___________
Circle
Parabola
Hyperbola
Ellipse
Explanation:
The poles of HN(s).HN(-s) is given by the characteristic equation 1+ϵ2TN2(s/j)=0.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
What is the number of maxima present in the pass band of magnitude frequency response of a low pass chebyshev-I filter of order 5?
1
2
3
4
Explanation:
In the magnitude frequency response of a low pass chebyshev-I filter, the pass band has 3 maxima and 2 minima(order 5=3 maxima+2 minima).