Digital Signal Processing

Design of IIR Filters from Analog Filters

Question 1
Marks : +2 | -2
Pass Ratio : 100%
For an analog LTI system to be stable, where should the poles of system function H(s) lie?
Right half of s-plane
Left half of s-plane
On the imaginary axis
At origin
Explanation:
An analog linear time invariant system with system function H(s) is stable if all its poles lie on the left half of the s-plane.
Question 2
Marks : +2 | -2
Pass Ratio : 100%
What is the duration of the unit sample response of a digital filter?
Finite
Infinite
Impulse(very small)
Zero
Explanation:
Digital filters are the filters which can be designed from analog filters which have infinite duration unit sample response.
Question 3
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?
y(n)=\\(\\sum_{k=0}^{M+1} b_k x(n+k)\\)
y(n)=\\(\\sum_{k=0}^{M+1} b_k x(n-k)\\)
y(n)=\\(\\sum_{k=0}^{M-1} b_k x(n-k)\\)
None of the mentioned
Explanation:
An FIR filter of length M with input x(n) and output y(n) is described by the difference equation
Question 4
Marks : +2 | -2
Pass Ratio : 100%
If the conversion technique is to be effective, the jΩ axis in the s-plane should map into the unit circle in the z-plane.
True
False
Explanation:
If the conversion technique is to be effective, the jΩ axis in the s-plane should map into the unit circle in the z-plane. Thus there will be a direct relationship between the two frequency variables in the two domains.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the condition on the system function of a linear phase filter?
H(z)=\\(z^{-N} H(z^{-1})\\)
H(z)=\\(z^N H(z^{-1})\\)
H(z)=\\(±z^N H(z^{-1})\\)
H(z)=\\(±z^{-N} H(z^{-1})\\)
Explanation:
A linear phase filter must have a system function that satisfies the condition
Question 6
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is a representation of system function?
Normal system function
Laplace transform
Rational system function
All of the mentioned
Explanation:
There are many ways how we represent a system function of which one is normal representation i.e., output/input and other ways like Laplace transform and rational system function.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
What is the relation between h(t) and Ha(s)?
Ha(s)=\\( \\int_{-\\infty}^{\\infty} h(t)e^{-st} dt\\)
Ha(s)=\\(\\int_0^{\\infty} h(t)e^{st} dt\\)
Ha(s)=\\( \\int_{-\\infty}^{\\infty} h(t)e^{st} dt\\)
None of the mentioned
Explanation:
We know that the impulse response h(t) and the Laplace transform Ha(s) are related by the equation.
Question 8
Marks : +2 | -2
Pass Ratio : 100%
Which of the following methods are used to convert analog filter into digital filter?
Approximation of Derivatives
Bilinear transformation
Impulse invariance
All of the mentioned
Explanation:
There are many techniques which are used to convert analog filter into digital filter of which some of them are Approximation of derivatives, bilinear transformation, impulse invariance and many other methods.
Question 9
Marks : +2 | -2
Pass Ratio : 100%
If the conversion technique is to be effective, then the LHP of s-plane should be mapped into _____________
Outside of unit circle
Unit circle
Inside unit circle
Does not matter
Explanation:
If the conversion technique is to be effective, then the LHP of s-plane should be mapped into the inside of the unit circle in the z-plane. Thus a stable analog filter will be converted to a stable digital filter.
Question 10
Marks : +2 | -2
Pass Ratio : 100%
Physically realizable and stable IIR filters cannot have linear phase.
True
False
Explanation:
If an IIR filter is stable and if it can be physically realizable, then the filter cannot have linear phase.