Digital signal and image processing FAQ

mukeshtekwani@outlook.com

Digital Signal and Image Processing
Frequently Asked Questions
In BE (Sem VII) – University of Mumbai
No

Question
JUSTIFY:
1. If the kernel of the image transform is separable and symmetric the transform
can be explained in matrix form. Justify.
2. Laplacian is not a good edge detector – Justify
3. Lossy compression is not suitable for compressing executable files – Justify
4.
5.
6.
7.

Low pass filter is a smoothing filter – Justify
Unit step sequence is a power signal – Justify
If the energy of a signal is finite, its power is zer. Justify
Laplacian is better than gradient for detection of edges – Justify

8. Walsh transform is nothing but sequently ordered Hadamard transform
matrix. Justify
9. All image compression techniques are invertible. Justify
10. For digital image having salt and pepper noise, median filter is best filter.
11. Unit ramp signal is neither energy nor power signal.
12. List and prove any four properties of DFT.
13. Find the circular convolution on the given two sequences x1(n) = {1, -1, 2, -4}
and x2(n) = {1, 2}
14. Compute the Hadamard of the image shown:
2
1
2
1
1
2
3
2
2
3
4
3
1
2
3
2
15. Give the classification of noise in images. Compare restoration and
enhancement. What are the differences between the two? What do they have
in common?
16. Three column vectors are given. Show that they are orthogonal. Also generate
all possible patterns. X1 = [1 1 1], x2 = [-2 1 1], x3 = [0 -1 1]
17. Explain image segmentation using thresholding. How to apply thresholding to
unevenly illuminated images?
18. What is image segmentation? Explain the following methods of image
segmentation. (i) Region growing , (ii) region splitting , (iii) thresholding
19. Determine the Z-transform of the following discrete time signals and also
specify the region of convergence (ROC)
(i) X(n) = {1*, 2, 3, 4},
(ii) X(n) = {1, 3, 5, 7*},
(iii) X(n) = {1, 2, 3, 4*, 5, 6, 7}
20. Explain log transformation. How is gamma correction done?
21. Find the Huffman code for the following stream of data (28 points)
{1,1,1,1,1,1,1, 2,2,2,2,2,2,2, 3,3,3,3,3, 4,4,4,4, 5,5,5, 6,6,7 }
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Marks

M/YY

5

D10

5
5

5

D10
D10
J12
D10
D10
D11
D11,
J12
D11

5
5
5
10
5

D11
J12
J12
D10
D10

5

D10

10

D10
J12

10

D10

10

D11

10
10

D10
J13
D10

10
10

D10
D10

5
5
5
5

22. What do you mean by Gaussian noise and why is averaging filter used to
eliminate it?
23. List down the advantages and disadvantages of Wiener filter.
24. Write short notes on
(i) KL transform (J13)
(ii) JPEG compression
(iii) Hough Transform
(iv) Classification of signals
(v) Discrete Cosine Transform (5) (D10) (J12) (J13)
(vi) Wiener filter (5) (2010)
(vii) Difference between low pass filter and median filter
(viii) Hough transform (5) (D10) (J12)
(ix) Homomorphic filter (5) (D10)
(x) 4,8,m connectivity of image pixels. (5) (D10)
(xi) Sampling and Quantization (5) (J12)
(xii) Wavelet transform (5) (J12)(J13)
(xiii) Properties of Fourier Transform (J13)

5

D10

5
10
each

D10

25.

10

D
2010

26. Obtain linear convolution of two discrete time signals as below:

10

D
2010

27. Find cross-correlation betweeen given signals
X(n) = {1, 2, 0*, 1} and y(n) = {4, 3, 2*, 1}

5

D
2010

28. Find Z transform of x(n) and draw its ROC

10

D
2010

29. Determine the auto corrrelation of the following signal x(n) = {1*, 3, 1, 1}

5

30. Using 4 point FFT algorithm, calculate the 2-D DFT of

10

D
2010
D10

31. Write 8 x 8 Hadamard transform matrix and its signal flow graph. Using the
butetrfly diagram, compute Hadamard transform for x(n) = {1, 2, 3, 4, 1, 2, 1, 2}
32. Perform histogram equalization and draw new equalized histogram of the
following image data
Gray
0
1
2
3
4
5
6
7
Level

10

D10

10

D11

2|Page

No of 790 1023 850
656 329 245
122 81
pixels
33. Equalize the given histogram. What happens when we equalize it twice?
Justify.
Grey Level
0
1
2
3
No. of pixels
70
20
7
3
34. Perform histogram equalization for following. Obtain a plot of original as well
as equalized histogram.
Intensity 0
1
2
3
4
5
6
7
No
of 70
100 40
60
0
80
10
40
pixels
35. Whatare the different types of redundancies in digital image? Explain in detail.
36. For the 3-bit 4x4 size image perform following operations.
(i) Thresholding T = 4
(ii) Intensity level slicing with background r1 = 2 and r2 = 5
(iii) bit plane slicing for MSB and LSB planes
(iv) Negation

37.

38.
39.
40.

41.

42.
43.

4
2
3
0
1
3
5
7
5
3
2
1
2
4
6
7
A causal FIR system has three cascaded block, first two of them have individual
impulse responses h1(n) = {1,2,2} h2(n) = u(n) – u(n-2). Find impulse response
of third block h3(n) if an overall impulse response is h(n) = {2, 5, 6, 3, 2, 2}
Explain in detail enhancement techniques used in Spatial domain used for
images.
Explain homomorphic filtering in detail.
Find the DFT of the given image:
0
1
2
1
1
2
3
2
2
3
4
3
1
3
2
3
Define
(i) Eucledean distance
(ii) City block distance
(iii) Chess board distance
(iv) m connectivity
Find the DFT of the given sequence (Use DITFFT algo) : x(n) = {1,2,3,4,4,3,2,1}
Given below is the table of 8 symbols and their frequency of coccurence. Give
the Huffman code for each symbol.

Symbol
S1
S2
S3
S4
S5
S6
S7
S8
Frequency 0.25 0.15 0.06 0.08 0.21 0.14 0.07 0.04
44. Perform the convolution of the following two sequences using Z transforms:
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10

D10

10

J12

10

D
2010
D
2010

10

10

J12

8

J12

6
6

J12
J12

10

J12

10
10

J12
J12

8

J12


45.
46.
47.
48.

X(n ) = (0.2) n and h(n) = (0.3) n u(n)
Find the inverse Z transform H(z) = 1/ [1 – 3z-1 + 0.5 z-2 ] , |z| > 1
Prove that two dimensional fourier transform matrix is an ordinary matrix.
Derive 8 directional Laplacian filter mask
Derive matrix representation of one dimensional Walsh tranbsform for N = 4
from forward Walsh transformation function.
State fidelity objective and and subjective criteria of image evaluation.
Derive the equation of contrast stretching transformation function on the
input image F and obtain the output image R.

6
5
5
5

J12
D12
D12
D12

5
6

D12
D12

8

D12

6

D12

6

D12

54. Segment the following image such that the difference between the maximum
intensity value and minimum intensity value in the segmente region is less
than 18 using split and merge technique.

8

J12

55. Let x(n) be four point sequence with x(k) = {1, 2, 3, 4}. Find the DFT of the
following sequence using X(k).
(i) P(n) = x(n) cos (nπ/2)
(ii) q(n) = 2∆(n) + 3 {Four point u(n) } + 4 x(n)

6

J12

49.
50.

51.

Given
,
(i) Find 3 bit IGS coded image and calculate compression factor and bits per
pixel (BPP).
(ii) Find decoded image and calculate MSK and PSNR.
52. Given h(n) = {1*, 2} find the response of the system to the input x(n) = {1, 2, 3}
using FFT and IFFT.
53.

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56.

8

D12

6

D12

6

D12

6

D12

8

D12

If the gray level intensity changes are to be made as shown in fig below, derive
the necessary expression for obtaining the new pixel value using slope.

(ii) Obtain the new image by applying the above mentioned transformation
function.
(iii) Plot the histogram of input and output image.
(iv) Compare the histogram of input and output image.
57.

Apply the folllowing filter mask W1, W2 and W3 on the input image F and
obtain the output image.
58. Given h(n) = (1/2)n u(n), find the response of the system to the input x(n) =
(1/4)n u(n) using Z transform method.
59. Explain trimmed average filter. Find trimmed average value of the input image
F at the center position for R = 2 and S = 1 wher R is the number of
consecutive pixels to be trimmed from the minimum extreme and S is the
number of consecutive pixels to be trimmed from maximum extreme.

60.

5|Page


(ii) Calculate bits per pixel (BPP) and percentage of compression of compressed
image. Donot consider the payload of Huffman table.
61. X(t) = sin(480πt) + 3 sin(720 πt) is sampled with Fs = 600 Hz.
(i) What are the frequencies in radians in the resulting DT signal x(n)?
(ii) If x(n) is passed through an ideal interpolator, what sithe reconstructed
signal?
62. Apply horizontal and vertical line detection mask on the following image F. Use
appropriate threshold value. Assume virtual rows and columns by repeating
border pixel values.

6

D12

6

D12

63. Assume that the edge in the gray level image starts in the first row and ends in
the last row. Find the cost of all possible edges using the following cost
function.
Cost (p, q) = Imax | f(p) – f(q)|
Where Imax is the max intensity value in the image and f(p) and f(q) are pixel
values at points p and q resp. Find the edge with the minimum value of cost.
Plot the graph.

8

D12

64.
65.
66.
67.
68.

5
5
5
5
5

D12
D12
D12
D12
J13

5

J13

5
5
10

J13
J13
J13

10

J13

69.
70.
71.
72.
73.

How to find inverse one dimensional DFT using forward DITFFT flowgraph.
Derive High Boost Filter mask (3 x3)
Bitreversal technique in FFT
Image enhancement using LOG transformation and power law trasformation.
Explain signals and systems with the help of suitable examples. Give
applications of signals and systems.
Find Z transform of the following finite duration signal and state its ROC: X(n) =
{1,2,5,7,0,1}
Given X(n) = {0, 1, 2, 3} find X(k) using DIT-FFT algorithm.
Find convolution of following signals: x(n) = {2, 1, 3, 5} and h(n) = {0, 1, 2, 4}
Determine the sytem function and unit sample response of the system given
by the diffference equation Y(n) = (1/2) Y(n-1) + 2 X(n)
Perform Histogram equalization for the following. Obtain a plot of original as
well as equalized histogram.
Grey
0
levels
No of 100
pixels

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1

2

3

4

5

6

7

90

50

20

0

0

0

0

74. Given x(n) = {0,1,2,3,4,5,6,7}, find x(k) using DIT-FFT algo.
75. Compute 2D DFT of given image using DIT-FFT algorithm.

10
10

J13
J13

76. Explain in detail enhancement techniques in spatial domain used for images.
77. What is HADAMARD transform? Write a 4x4 Hadamard matrix and its
applications.
78. Explain image restoration and its applications.
79. What do you understand by sampling and quantization with respect to digital
image pocessing? How will you convert an analog image into a digital image?
80. Name and explain different types of redundancies associated with digital
image.

10
10

J13
J13

10
10

J13
J13

10

J13

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Digital signal and image processing FAQ

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