CS2403 - Digital Signal Processing
Important
Questions Nov/Dec 2012
POSSIBLE 2 TWO MARKS QUESTIONS(UNIT I-V)
1. What is
meant by aliasing? How can it be avoided?
2. Find the
energy and power of x(n) = Aejωn u(n).
3. Determine
which of the following sequences is periodic, and compute their fundamental
period. (a) Aej7πn (b) sin(3n)
4. Is the
system y (n) = ln [x (n)] is linear and time invariant?
5. Determine
Z transform of x(n) = 5nu(n)
6. State
sampling theorem.
7. Find the
signal energy of (1/2)n u(n)
8. Determine
whether the following sinusoids is periodic, if periodic then compute their
fundamental period. (a) cos 0.01πn (b) sin(π62n/10)
9. Check
whether the system y(n) = ex (n) is linear.
10. Determine
Z transform of x(n) = anu(n)
11. How DFT is
differ from DTFT
12. Find DFT
of sequence x(n) = {1, 1, -2, -2}
13. What are
the computational saving (both complex multiplication and complex addition) in
using N – point FFT algorithm.
14. What
do you mean by in – place computation?
15. Differentiate
between DIT and DIF FFT algorithm.
16. Write DFT
pair of equation
17. List any
four properties of DFT.
18. Compute
DFT of x(n) = {1, -1, 1, -1}
19. Calculate
% saving in computing through radix – 2, DFT algorithm of DFT coefficients.
Assume N = 512.
20. Find the
value of WNK when N = 8 and K = 2 and also k = 3
21. What are
the advantages of FIR filters?
22. What are
the desirable characteristics of windows?
23. Define
Phase Delay and Group Delay.
24. Draw the
Direct form I structure of the FIR filter.
25. Compare
FIR and IIR digital filter
26. Draw the
ideal gain Vs frequency characteristics of HPF and BPF.
27. What is
Gibb’s phenomenon?
28. Write the
steps involved in FIR filter design.
29. List out
the different forms of structural realizations available for realizing a FIR
system.
30. Use the
backward difference for the derivative
and convert the analog filter to digital filter given H(s)=1/(s2 +16)
31. State the
relationship between the analog and digital frequencies when converting an
analog filter using bilinear transformation.
32. Explain
the advantage and drawback of Bilinear
transformation
33. Explain
the term “ wrapping effect”
34. Find the
transfer function for normalized butterworth filter of order 1 by determining
the pole values.
35. Find
digital filter equivalent for H(s)=1/(s+8)
36. Sketch the
mapping of s – plane and z – plane in bilinear transformation.
37. Represent
decimal number 0.69 in fixed point representation of length N = 6
38. What is
Vocoder.
39. What are
the different formats of fixed point representation?
40. State a
few applications of adaptive filter
POSSIBLE 16 SIXTEEN MARKS QUESTIONS(UNIT I-V)
41. (i) Find the
convolution of the signals x(n) = and
h(n) = u(n) . (8)
(ii) Consider a system y(n) + y(n – 1) = x(n) + x(n – 1). Find transfer function, and
impulse response the system. (8)
42. (i) Find
inverse Z – transfer of
X(Z) = if
(1) ROC : |Z|
> 1, (2) ROC : |Z| < 0.5, (3) ROC : 0.5 < |Z| <1 (12).
(ii) Derive expressions to relate Z – transfer and DFT (4)
43. (i)Determine
the transfer function, and impulse response of the system y(n) – y(n – 1) +
y(n – 2) = x(n) + x(n – 1). (8)
(ii) Find the convolution sum of
and h(n) = δ(n) – δ(n – 1) + δ(n – 2) – δ(n – 3). (8)
44. (i) Find
the Z transform of (4 + 4)
(1) x(n) = 2n
u(n – 2)
(2) x(n) = n2
u(n)
(ii) State and explain the scaling and time delay properties
of Z transform. (8)
45. (i)
Discuss the properties of DFT. (10)
(ii) State and prove the circular convolution property of
DFT. (6)
46. (i)
Compute DFT of following sequence (6)
(1)
x(n) = {1, 0, -1, 0}
(2)
x(n) = {j, 0, j, 1}
(ii)
Using DFT and IDFT method, perform circular convolution of the sequence x(n) = {1, 2, 2, 1} and h(n) =
{1, 2, 3}. (10)
47. Find DFT
of the sequence x(n) = { 1, 1, 1, 1, 1, 1, 0, 0} using radix -2 DIF – FFT algorithm. (16)
48. Compute
the eight point DFT of the given sequence x(n) = { ½, ½, ½, ½, 0, 0, 0, 0}
using radix – 2 DIT - DFT algorithm. (16)
49. (i)Design
digital low pass filter using BLT. Given that
Assume sampling frequency of 100 rad/ sec. (8)
(ii)
Design IIR filter using impulse invariance technique. Given that and
implement the resulting digital
filter by adder, multipliers and delays. Assume sampling period =1sec. (8)
50. (i) Obtain
the direct form1, canonic form and parallel form realization structures for the
system given by the
difference equation
( ) = – 0 .1 (
– 1) + 0.72 ( – 2) + 0.7 ( ) – 0.252 ( –
2). (10)
(ii) If find using impulse invariant method for sampling
frequency of 5 samples/sec (6)
51. Design
butterworth filter using bilinear transformation method for the following
specifications
0.8 ≤ |H(ejω)| ≤ 1; 0 ≤ ω ≤ 0.2π
|H(ejω)| ≤ 0.2; 0.6 ≤ ω ≤ π (16)
52. Design an
IIR digital low pass butterworth filter to meet the following requirements:
Pass band ripple (peak to peak): ≤ 0.5dB, Pass band edge: 1.2kHz, Stop band
attenuation: ≥ 40dB, Stop band edge: 2.0 kHz, Sampling rate: 8.0 kHz. Use
bilinear transformation technique. (16)
53. Design a
symmetric FIR low pass filter whose desired frequency is given as
( ) =
The
length of the filter should be 7 and =
1 rad / sample. Use rectangular window. (16)
54. (i)For a
FIR linear phase digital filter approximating the ideal frequency response
( ) =
Determine
the coefficients of a 5 tap filter using rectangular window. (8)
(ii)
Determine unit sample response ( ) of a
linear phase FIR filter of length M = 4 for which
the frequency response at and is given as
r(0) = 1 and
r( (8)
55. (i)
Determine the coefficients h(n) of a linear phase FIR filter of length M = 15
which has a symmetric unit
sample response and a frequency response (12)
Hr =
(ii) State the advantage of floating point representation
over fixed points representation.(4)
56. (i)Determine
the first 15 coefficients of FIR filters of magnitude specification is given
below using frequency sampling method:
( ) = (12)
(ii) Discuss the effect of finite word length on digital
filter. (4)
57. With neat
diagram and supportive derivation explain multirate signal processing using two
techniques. (16)
58. (i)Explain
decimation of sampling rate by an integer factor D and derive spectra for
decimated signal. (10)
(ii) Discuss on sampling rate conversion of rational factor
I/D (6)
59. Write
short notes on (a) Image enhancement (b) Speech Processing (c) Musical sound
processing and (d) vocoder. (16)
60. What is
adaptive filter? With neat block diagram discuss any four applications of
adaptive filter. (16)
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