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# Digital signal and image processing FAQ

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Digital Signal and Image Processing - FAQ
BE -Sem 7, University of Mumbai
Frequently asked questions in BE Sem 7 examinations of University of Mumbai, with marks for each question, month and year of exam.

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### Digital signal and image processing FAQ

1. 1. 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 } 1|Page 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
2. 2. mukeshtekwani@outlook.com 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
3. 3. mukeshtekwani@outlook.com 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: 3|Page 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
4. 4. mukeshtekwani@outlook.com 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. 4|Page
5. 5. mukeshtekwani@outlook.com 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
6. 6. mukeshtekwani@outlook.com (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 6|Page 1 2 3 4 5 6 7 90 50 20 0 0 0 0
7. 7. mukeshtekwani@outlook.com 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 7|Page