IMPORTANT QUESTIONS - EC6502 Principles of Digital Signal Processing-2
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)
Comments
Post a Comment