1. In which of the following transformations, poles, and zeros of H(s) are mapped directly into poles and zeros in the z-plane?
A. Impulse invariance
B. Bilinear transformation
C. Approximation of derivatives
D. Matched Z-transform
Answer: D
In this method of transforming an analog filter into an equivalent digital filter is to map the poles and zeros of H(s) directly into poles and zeros in the z-plane.
2. Which of the following is true in matched z-transform?
A. Poles of H(s) are directly mapped to poles in z-plane
B. Zeros of H(s) is directly mapped to poles in z-plane
C. Poles & Zeros of H(s) are directly mapped to poles in z-plane
D. None of the mentioned
Answer: C
In the transformation of the analog filter into the digital filter by matched z-transform method, the poles and zeros of H(s) directly into poles and zeros in the z-plane.
3. In matched z-transform, the poles and zeros of H(s) are directly mapped into poles and zeros in the z-plane.
A. True
B. False
Answer: A
In this method of transforming an analog filter into an equivalent digital filter is to map the poles and zeros of H(s) directly into poles and zeros in the z-plane.
4. The factor of the form (s-A. in H(s) is mapped into which of the following factors in the z-domain?
A. 1-eaTz
B. 1-eaTz-1
C. 1-e-aTz-1
D. 1+eaTz-1
Answer: B
If T is the sampling interval, then each factor of the form (s-A. in H(s) is mapped into the factor (1-eaTz-1) in the z-domain.
5. The factor of the form (s+A. in H(s) is mapped into which of the following factors in the z-domain?
A. 1-eaTz
B. 1-eaTz-1
C. 1-e-aTz-1
D. 1+eaTz-1
Answer: C
If T is the sampling interval, then each factor of the form (s+A. in H(s) is mapped into the factor (1-e-aTz-1) in the z-domain.
6. If the factor of the form (s-A. in H(s) is mapped into 1-eaTz-1 in the z-domain, that kind of transformation is called ______
A. Impulse invariance
B. Bilinear transformation
C. Approximation of derivatives
D. Matched Z-transform
Answer: D
If T is the sampling interval, then each factor of the form (s-A. in H(s) is mapped into the factor (1-eaTz-1) in the z-domain. This mapping is called the matched z-transform.
7. The poles obtained from matched z-transform are identical to poles obtained from which of the following transformations?
A. Bilinear transformation
B. Impulse invariance
C. Approximation of derivatives
D. None of the mentioned
Answer: B
We observe that the poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method.
8. The zero positions obtained from matched z-transform and impulse invariance methods are not the same.
A. True
B. False
Answer: A
We observe that the poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method. However, the two techniques result in different zero positions.
9. The sampling interval in the matched z-transform must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.
A. True
B. False
Answer: A
To preserve the frequency response characteristic of the analog filter, the sampling interval in the matched z-transformation must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.
11. What should be the value of sampling interval T, to avoid aliasing?
A. Zero
B. Sufficiently large
C. Sufficiently small
D. None of the mentioned
Answer: C
Aliasing in this matched z-transformation can be avoided by selecting the sampling interval T sufficiently small.
12. Low pass Butterworth filters are also called as ________
A. All-zero filter
B. All-pole filter
C. Pole-zero filter
D. None of the mentioned
Answer: B
Low pass Butterworth filters are also called all-pole filters because it has only non-zero poles.
13. What is the equation for the magnitude square response of a low pass Butterworth filter?
A. \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)
B. \(1+(\frac{Ω}{Ω_C})^{2N}\)
C. \(\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}\)
D. None of the mentioned
Answer: A
A Butterworth is characterized by the magnitude frequency response
Thus by substituting the corresponding values in the above equation, we get N=6.64
To meet the desired specifications, we select N=7.
17. Which of the following is true about the type-1 Chebyshev filter?
A. Equi-ripple behavior in passband
B. Monotonic characteristic in stopband
C. Equi-ripple behavior in passband & Monotonic characteristic in stopband
D. None of the mentioned
Answer: C
Type-1 Chebyshev filters are all-pole filters that exhibit equi-ripple behavior in the passband and a monotonic characteristic in the stopband.
18. Type-2 Chebyshev filters consists of ______________
A. Only poles
B. Both poles and zeros
C. Only zeros
D. Cannot be determined
Answer: B
Type-1 Chebyshev filters are all-pole filters whereas the family of type-2 Chebyshev filters contains both poles and zeros.
19. Which of the following is false about the type-2 Chebyshev filters?
A. Monotonic behavior in the passband
B. Equi-ripple behavior in the stopband
C. Zero behavior
D. Monotonic behavior in the stopband
Answer: D
Type-2 Chebyshev filters exhibit equi-ripple behavior in the stopband and a monotonic characteristic in the passband.
20. The zeros of type-2 class of Chebyshev filters lies on ___________
A. Imaginary axis
B. Real axis
C. Zero
D. Cannot be determined
Answer: A
The zeros of this class of filters lie on the imaginary axis in the s-plane.
21. Which of the following defines a Chebyshev polynomial of order N, TN(x)?
A. cos(Ncos-1x) for all x
B. cosh(Ncosh-1x) for all x
C.cos(Ncos-1x), |x|≤1 cosh(Ncosh-1x), |x|>1
D. None of the mentioned
Answer: C
In order to understand the frequency-domain behavior of Chebyshev filters, it is of utmost importance to define a Chebyshev polynomial and then its properties. A Chebyshev polynomial of degree N is defined as
TN(x) = cos(Ncos-1x), |x|≤1
cosh(Ncosh-1x), |x|>1
22. The frequency response shown in the figure below belongs to which of the following filters?
A. Type-1 Chebyshev
B. Type-2 Chebyshev
C. Butterworth
D. Elliptical
Answer: B
Since the passband is monotonic in behavior and the stopband exhibit equi-ripple behavior, it is the magnitude square response of a type-2 Chebyshev filter.
23. What is the order of the type-2 Chebyshev filter whose magnitude square response is as shown in the following figure?
A. 2
B. 4
C. 6
D. 3
Answer: D
Since the magnitude square response of the type-2 Chebyshev filter, it has an odd number of maxima and minima in the stopband, the order of the filter is odd i.e., 3.
24. Which of the following is true about the magnitude square response of an elliptical filter?
A. Equi-ripple in passband
B. Equi-ripple in stopband
C. Equi-ripple in passband and stopband
D. None of the mentioned
Answer: C
An elliptical filter is a filter that exhibits equi-ripple behavior in both passband and stopband of the magnitude square response.
25. Bessel filters exhibit a linear phase response over the passband of the filter.
A. True
B. False
Answer: A
An important characteristic of the Bessel filter is the linear phase response over the passband of the filter. As a consequence, Bessel filters have a larger transition bandwidth, but their phase is linear within the passband.
