Digital Signal Processing

IIR Filter Design by Approximation of Derivatives

Question 1
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the backward difference for the derivative of y(t) with respect to ‘t’ for t=nT?
[y(n)+y(n+1)]/T
[y(n)+y(n-1)]/T
[y(n)-y(n+1)]/T
[y(n)-y(n-1)]/T
Explanation:
For the derivative dy(t)/dt at time t=nT, we substitute the backward difference [y(nT)-y(nT-T)]/T. Thus
Question 2
Marks : +2 | -2
Pass Ratio : 100%
Which of the following mapping is true between s-plane and z-domain?
Points in LHP of the s-plane into points inside the circle in z-domain
Points in RHP of the s-plane into points outside the circle in z-domain
Points on imaginary axis of the s-plane into points onto the circle in z-domain
All of the mentioned
Explanation:
The below diagram explains the given question
Question 3
Marks : +2 | -2
Pass Ratio : 100%
It is possible to map the jΩ-axis into the unit circle.
True
False
Explanation:
By proper choice of the coefficients of {αk}, it is possible to map the jΩ-axis into the unit circle.
Question 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following filter transformation is not possible?
High pass analog filter to low pass digital filter
High pass analog filter to high pass digital filter
Low pass analog filter to low pass digital filter
None of the mentioned
Explanation:
We know that only low pass and band pass filters with low resonant frequencies in the digital can be designed. So, it is not possible to transform a high pass analog filter into a corresponding high pass digital filter.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
An analog filter can be converted into digital filter by approximating the differential equation by an equivalent difference equation.
True
False
Explanation:
One of the simplest methods for converting an analog filter into digital filter is to approximate the differential equation by an equivalent difference equation.
Question 6
Marks : +2 | -2
Pass Ratio : 100%
If s=jΩ and if Ω varies from -∞ to ∞, then what is the corresponding locus of points in z-plane?
Circle of radius 1 with centre at z=0
Circle of radius 1 with centre at z=1
Circle of radius 1/2 with centre at z=1/2
Circle of radius 1 with centre at z=1/2
Explanation:
We know that
Question 7
Marks : +2 | -2
Pass Ratio : 100%
What is the second difference that is used to replace the second order derivate of y(t)?
[y(n)-2y(n-1)+y(n-2)]/T
[y(n)-2y(n-1)+y(n-2)]/T2
[y(n)+2y(n-1)+y(n-2)]/T
[y(n)+2y(n-1)+y(n-2)]/T2
Explanation:
We know that dy(t)/dt =[ y(n)-y(n-1)]/T
Question 8
Marks : +2 | -2
Pass Ratio : 100%
This mapping is restricted to the design of low pass filters and band pass filters having relatively small resonant frequencies.
True
False
Explanation:
The possible location of poles of the digital filter are confined to relatively small frequencies and as a consequence, the mapping is restricted to the design of low pass filters and band pass filters having relatively small resonant frequencies.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
Which of the following in z-domain is equal to s-domain of second order derivate?
\\((\\frac{1-z^{-1}}{T})^2\\)
\\((\\frac{1+z^{-1}}{T})^2\\)
\\((\\frac{1+z^{-1}}{T})^{-2}\\)
None of the mentioned
Explanation:
We know that for a second order derivative
Question 10
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is true relation among s-domain and z-domain?
s=(1+z-1)/T
s=(1+z )/T
s=(1-z-1)/T
None of the mentioned
Explanation:
The analog differentiator with output dy(t)/dt has the system function H(s)=s, while the digital system that produces the output [y(n)-y(n-1)]/T has the system function H(z) =(1-z-1)/T. Thus the relation between s-domain and z-domain is given as