Digital Signal Processing Multiple Choice Questions on “Design of IIR Filters from Analog Filters”.
1. What is the duration of the unit sample response of a digital filter?
A. Finite
B. Infinite
C. Impulse(very small)
D. Zero
Answer: B
Clarification: Digital filters are the filters which can be designed from analog filters which have infinite duration unit sample response.
2. Which of the following methods are used to convert analog filter into digital filter?
A. Approximation of Derivatives
B. Bilinear transformation
C. Impulse invariance
D. All of the mentioned
Answer: D
Clarification: 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.
3. Which of the following is the difference equation of the FIR filter of length M, input x(n) and output y(n)?
A. y(n)=(sum_{k=0}^{M+1} b_k x(n+k))
B. y(n)=(sum_{k=0}^{M+1} b_k x(n-k))
C. y(n)=(sum_{k=0}^{M-1} b_k x(n-k))
D. None of the mentioned
Answer: C
Clarification: An FIR filter of length M with input x(n) and output y(n) is described by the difference equation
y(n)=(sum_{k=0}^{M-1} b_k x(n-k))
where {bk} is the set of filter coefficients.
4. What is the relation between h(t) and Ha(s)?
A. Ha(s)=( int_{-infty}^{infty} h(t)e^{-st} dt)
B. Ha(s)=(int_0^{infty} h(t)e^{st} dt)
C. Ha(s)=( int_{-infty}^{infty} h(t)e^{st} dt)
D. None of the mentioned
Answer: A
Clarification: We know that the impulse response h(t) and the Laplace transform Ha(s) are related by the equation.
Ha(s)=( int_{-infty}^{infty} h(t)e^{-st} dt).
5. Which of the following is a representation of system function?
A. Normal system function
B. Laplace transform
C. Rational system function
D. All of the mentioned
Answer: D
Clarification: 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.
6. For an analog LTI system to be stable, where should the poles of system function H(s) lie?
A. Right half of s-plane
B. Left half of s-plane
C. On the imaginary axis
D. At origin
Answer: B
Clarification: 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.
7. 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.
A. True
B. False
Answer: A
Clarification: 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.
8. If the conversion technique is to be effective, then the LHP of s-plane should be mapped into _____________
A. Outside of unit circle
B. Unit circle
C. Inside unit circle
D. Does not matter
Answer: C
Clarification: 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.
9. Physically realizable and stable IIR filters cannot have linear phase.
A. True
B. False
Answer: A
Clarification: If an IIR filter is stable and if it can be physically realizable, then the filter cannot have linear phase.
10. What is the condition on the system function of a linear phase filter?
A. H(z)=(z^{-N} H(z^{-1}))
B. H(z)=(z^N H(z^{-1}))
C. H(z)=(±z^N H(z^{-1}))
D. H(z)=(±z^{-N} H(z^{-1}))
Answer: D
Clarification: A linear phase filter must have a system function that satisfies the condition
H(z)=(±z^{-N} H(z^{-1}))
where z(-N) represents a delay of N units of time.
11. If the filter is in linear phase, then filter would have a mirror-image pole outside the unit circle for every pole inside the unit circle.
A. True
B. False
Answer: A
Clarification: For a linear phase filter, we know that
H(z)=(±z^{-N} H(z^{-1}))
where z(-N) represents a delay of N units of time. But if this were the case, the filter would have a mirror image pole outside the unit circle for every pole inside the unit circle. Hence the filter would be unstable.
12. What is the order of operations to be performed in order to realize linear phase IIR filter?
(i) Passing x(-n) through a digital filter H(z)
(ii) Time reversing the output of H(z)
(iii) Time reversal of the input signal x(n)
(iv) Passing the result through H(z)
A. (i),(ii),(iii),(iv)
B. (iii),(i),(ii),(iv)
C. (ii),(iii),(iv),(i)
D. (i),(iii),(iv),(ii)
Answer: B
Clarification: If the restriction on physical reliability is removed, it is possible to obtain a linear phase IIR filter, at least in principle. This approach involves performing a time reversal of the input signal x(n), passing x(-n) through a digital filter H(z), time reversing the output of H(z), and finally, passing the result through H(z) again.
13. When an application requires a linear phase filter, it should be an FIR filter.
A. True
B. False
Answer: A
Clarification: The signal processing is computationally cumbersome and appear to offer no advantages over linear phase FIR filters. Consequently, when an application requires a linear phase, it should be an FIR filter.