Question Paper: Digital Signal Processing : Question Paper May 2014 - Computer Engineering (Semester 7) | Mumbai University (MU)
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## Digital Signal Processing - May 2014

### Computer Engineering (Semester 7)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1 (a) Laplacian is not good edge detector. Justify.(5 marks) 1 (b) Discuss the properties of Region of Convergence.(5 marks) 1 (c) Convolution in one domain leads to multiplication in other domain.(5 marks) 1 (d) Walsh transform is nothing but sequence Orderd Hadamard Transform Matrix Justify.(5 marks) 2 (a) Construct following gray scale quantization code for given level data set.
{100, 110, 124, 130, 200, 210}
(10 marks)
2 (b) Find the following sequence are periodic or no. If yes, find the fundamental time period-
(i) x1(n)=3sin(0.01 ?n)+4cos(10 n)
(ii) x2=cos(0.01 ?n)
(10 marks)
3 (a) Determine the system function and unit sample response of the given system described by following difference equations :
$$y(n)= \frac{1}{4} y(n-2)+\frac{1}{2}y(n-1)+x(n)$$
(10 marks)
3 (b) Find cross-correlation between given signals.
x(n)={1,0,1,2}
y(n)={1,2,3,4}
(5 marks)
3 (c) Find auto-correlation of following signal
x(n)={1,1,2,3}
(5 marks)
4 (a) Compute DFT of the given image using DIF-FFT technique

 0 1 2 1 1 2 3 2 2 3 4 3 1 2 3 2
(10 marks) 4 (b) Explain the process of image segmentaion using different methods.(10 marks) 5 (a) Specify DCT basis functions and construct transform matrix for an image.(10 marks) 5 (b) Obtain the digital negative of the following 8 bits per pixel image.
 121 205 217 156 151 139 127 157 117 125 252 117 236 138 142 227 182 178 197 242 201 106 119 251 240
(10 marks)
6 (a) Perform Histogram Equalization on the given image transform
 Gray Level 0 1 2 3 4 5 6 7 Number of Pixel 70 100 40 80 60 40 08 02
(10 marks)
6 (b) Write 8 x 8 Walsh transform matrix and draw its signal flow graph(10 marks)

### Write short noes on (any four) :-

7 (a) Hough transform(5 marks) 7 (b) Wavelet Transform(5 marks) 7 (c) Classify and define discrete time systems(5 marks) 7 (d) Homomorphic filtering.(5 marks) 7 (e) State and prove convolution property of Z-transform.(5 marks)