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2013 REGULATION
ANNA UNIVERSITY QUESTIONS
ECE
ENGINEERING NOTES
EVENTUALENGINEER
Principles of Digital Signal Processing
QUESTIONS
Question Bank
Unit – II
Part – A
1. Distinguish between analog and digital filter.
2. What are the advantages of digital filter over analog filter?
3. Give the Magnitude function of Butterworth filter. What is the effect of varying order of N on magnitude and phase response?
4. Give any two properties of Butterworth low pass filter.
5. What are the properties of chebyshev filter?(Apr-2011,Nov-2011)
6. Give the equation for the order N and cut off frequency Ωc of Butterworth filter.
7. Given the specification αp = 1dB; αs = 30dB; Ωp = 200 rad/sec; Ωs = 600 rad/sec. Determine the order of the Butterworth filter. (Ans: N = 4)
8. Give the chebyshev filter transfer function and its magnitude response.
9. Distinguish between the frequency response of Chebyshev type I and type II filters.
10. Give the equation for the order N of Chebyshev filter.
11. Given the specification αp = 3dB; αs = 16dB; fp = 1KHz; fs = 2KHz. Determine the order of the Chebyshev filter. (Ans: N = 2)
12. Distinguish between Butterworth and Chebyshev (type I) filters.
13. How one can design digital filters from analog filters
H(s) = (s + 0.2)
(s + 0.2)2 + 9
Use the impulse invariant technique. Assume T = 1s.
Ans: H(z) = 1 + 0.811z-1
(1+ 1.621 z-1+ 0.671 z-2)
14. For the analog transfer function
H(s) = 1
(s + 1) (s + 2)
Determine H(z) using impulse invariant technique. Assume T = 1s.(Nov-2011)
Ans: H(z) = 0.2326z-1
(1 - 0.503z-1 + 0.0498 z-2)
15. Mention any two procedure for digitizing the transfer function of an analog filter?(Nov-2013)
16. What are the properties that are maintained same in the transfer of analog filter into a digital filter?
17. What is meant by impulse invariant method of designing IIR filter?
18. By impulse invariant method obtain the digital filter transfer function and the differential equation of analog filter H(s) = 1/(s + 1).
19. Obtain the impulse response of digital filter corresponding to an analog filter with impulse response ha(t) = 0.5e-2t u(t) and with a sampling rate of 1Hz using impulse invariant method.
20. Why impulse invariant method is not preferred in the design of IIR filter other than low pass filter?
21. Give the bilinear transformation equation between s-plane and z-plane.
22. Using bilinear transformation obtain H(z) if H(s) = 1 / (s + 1)2 and T = 0.1s.
Ans: H(z) = 0.0476(1 + z-1)2
(1 - 0.9048 z-1)2
23. What are the properties of the bilinear transformation?
24. What is warping effect?
25. Write short notes on prewarping. (Nov-2014,Nov-2010,May-2012)
26. Distinguish between recursive and non-recursive realisation.
27. What are the advantages and disadvantages of bilinear transformation?(May-2014)
28. What are the different types of realization structures for realisation of IIR systems?
29. Draw the general realization structure in direct form I and II of IIR system.
30. Give direct form I and direct form II structure of 2nd order system.
31. How many number of addition, multiplication delay blocks are required to realize a system H(z) having M zeros and N poles in (a) direct form I and (b) direct form II realization?
32. What is the main advantage of direct form II realization when compared to direct form I realization?(Nov-2011,Nov-2013,Nov-2010)
33. What is transposed structure?
34. Give the transposed direct form II structure of IIR 2nd order.
35. Realize y(n) + y(n-1) + 0.25y(n-2) = x(n) in cascade form.
36. What is the advantage of cascade realization? (Hint: Quantization error can be reduced).
Part – B
1. Design an analog Butterworth filter that has a -2dB of passband attenuation at a frequency of 20 rad/sec and atleast -10dB stopband attenuation at a frequency of 30 rad/sec.
Ans: N = 4
H(s) = 0.2092 x 106
(s2 + 16.389s + 457.394) (s2+ 39.518s + 457.394)
2. For the given specifications, design an analog Butterworth filter,
0.9 <|H(jΩ)| < 1, 0 <Ω < 0.2π
|H(jΩ)| <0.2, 0.4π < Ω <π
Ans: N = 4
H(s) = 0.323
(s2 + 0.577s + 0.0576π2) (s2 + 1.393s + 0.0576π2)
3. Design a Chebyshev filter with a maximum passband attenuation of 2.5dB at Ωp = 20rad/sec and stopband attenuation of 30dB at Ωp = 50rad/sec.
Ans: N = 3
H(s) = 2265.27
(s + 6.6) (s2+ 6.6s + 343.2)
4. Using impulse invariant method with T = 1s, determine H(z) if H(s) = 1/( s2+√2s+1).
Ans: H(z) = 0.453z-1
(1 – 0.7497 z-1+ 0.2432 z-2)
5. For the analog transfer function H(s) = 2 / (s+1)(s+2), determine H(z) using impulse invariance method. Assume T=1s.
Ans: H(z) = 0.465z-1
(1 – 0.503 z-1+ 0.05 z-2)
6. Design a 3rd order Butterworth digital filter using impulse invariant technique. Assume sampling period T = 1s.(Nov-2011)
Ans: H(z) = 1 + (-1 + 0.453z-1)
(1 – 0.368z-1) (1 – 0.786 z-1+ 0.368 z-2)
7. An analog filter has a transfer function H(s) = 10 / (s2 + 7s + 10). Design a digital filter equivalent to this using impulse invariant method for T = 0.2s.
Ans: H(z) = 0.201z-1
(1 – 1.378 z-1+ 0.247 z-2)
8. Apply bilinear transformation to H(s) = 2 / (s+1)(s+2) with T = 1s and find H(z).
Ans: H(z) = 0.166 (1+z-1)2
(1 – 0.33 z-1)
9. Determine H(z) that results when the bilinear transformation is applied to
H(s) = (s2 +4.525)
(s2 + 0.692s + 0.504)
Ans: H(z) = 1.448 + 0.1783z-1 + 1.448z-2
(1 – 1.1875 z-1+ 0.5299 z-2)
10. Obtain the direct form I an direct form II realization structure for the system described by the following difference equation
- y(n) = 0.5 y(n-1) – 0.25 y(n-2) + x(n) + 0.4 x(n-1).
- y(n) = -0.1 y(n-1) + 0.72 y(n-2) + 0.7x(n) - 0.252 x(n-2).
11. Obtain the direct form I, direct form II, cascade and parallel form realization for the system y(n) = -0.1 y(n-1) + 0.2 y(n-2) + 3x(n) + 3.6 x(n-1) + 0.6 x(n-2).(Nov-2011,Nov-2014,May-2014,Nov-2010,May-2012)
12. Obtain the cascade and parallel realization for the following systems
- H(z) = (1 + 1.5z-1 + 0.5z-2) ( 1 - 1.5z-1 + z-2)
(1 + z-1 + 0.25z-2) ( 1 + 0.25z-1 + 0.5z-2)
- H(z) = (1 - 0.5z-1) ( 1 - 0.5z-1 + 0.25z-2)
(1 + 0.25z-1) (1 + z-1 + 0.5z-2) ( 1 - 0.25z-1 + 0.5z-2)
13. Design a digital Butterworth filter satisfying the constraint(Nov-2011,May-2012)
0.707 < |H(jΩ)| < 1, 0 <Ω < π/2
|H(jΩ)| < 0.2, 3π/4 <Ω < π
With T=1s using (a) Bilinear transformation (b) impulse invariant. Realize the fiter in each case using the most convenient realization form.
(a) Ans: N = 2
H(s) = 4
(s2 + 2.828s + 4)
H(z) = 0.293 (1+z-1)2
(1 + 0.172z-1)
(b) Ans: N = 4
H(s) = (1.57)4
(s2 + 1.202s + 2.465) (s2 + 2.902s + 2.465)
H(z) = (1.454 + 0.184z-1) + (-1.454 + 0.231z-1)
(1 – 0.387 z-1 + 0.055 z-2) (1 – 0.132 z-1 + 0.301 z-2)
14. Design a Chebyshev low pass filter with specifications αp = 1dB ripple in the passband 0 ≤ ω ≤ 0.2π, αs= 15dB ripple in the stopband 0.3π ≤ ω ≤ π, using (a) bilinear transformation and (b) impulse invariant method.(Nov-2014,Nov-2010)
(a) Ans: N = 4
H(s) = 0.0438
(s2 + 0.1814s + 0.4165) (s2 + 0.4378s + 0.118)
H(z) = 0.0018(1 + z-1)4
(1 – 1.499 z-1 + 0.848 z-2) (1 – 1.555 z-1 + 0.649 z-2)
(b) Ans: N = 4
H(s) = 0.0383
(s2 + 0.175s + 0.391) (s2 + 0.423s + 0.11)
H(z) = (-0.083 - 0.025z-1) + (0.083 + 0.0238z-1)
(1 – 1.49 z-1 + 0.839z-2) (1 – 1.56 z-1 + 0.655 z-2)
15. Design a digital Chebyshev filter to satisfy the constraint
0.707 < |H(jΩ)| < 1, 0 <Ω < 0.2π
|H(jΩ)| < 0.1, 0.5π <Ω < π
Using bilinear transformation and assuming T = 1s.
Ans: N = 2
H(s) = 0.2111
(s2 + 0.418s + 0.2985)
H(z) = 0.041(1 + z-1)2
(1 – 1.4418 z-1 + 0.6743 z-2)
16. Discuss the steps in the design of IIR filter using BLT method.(Nov-2013,May-2012)
17. Determine H(z) for a Butterworth filter satisfying the following
√0.5 <|H(jΩ)| < 1, 0 <Ω < π/2
|H(jΩ)| < 0.2, 3π/4 <Ω < π
With T = 1s. Apply impulse invariant transformation.
Ans: N = 4
H(s) = 6.086
(s2 + 1.2022s + 2.467) (s2 + 2.903s + 2.467)
H(z) = (-1.451 - 0.232z-1) + (1.451 + 0.185z-1)
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