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Digital Signal Processing : Question Paper May 2015 - Computer Engineering (Semester 7) | Mumbai University (MU)

## Digital Signal Processing - May 2015

### 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.

### Solve any five:

1 (a) Check unit step signal for energy power signal and find its value. (4 marks)

1 (b) Find DFT of x(n)={3,1,2,4} using DIF-FFT. (4 marks)

1 (c) Compare between lossy and lossless compression. (4 marks)

1 (d) Explain image fidelity criterion. (4 marks)

1 (e) Find Z.T. of $$x(n)= {2, \underset {\uparrow}{1}, 0, 3, 4}$$ . Find ROC of x(z). (4 marks)

1 (f) Prove that 2D DFT matrix is an unitary matrix. (4 marks)

2 (a) Find the circular convolution of the two sequence. (5 marks)

2 (b) "Find The DFT of the given image: $$\begin{bmatrix} 0 &1 &2 &1 \\1 &2 &3 &2 \\2 &3 &4 &3 \\1 &2 &3 &2 \end{bmatrix}$$" (5 marks)

2 (c) Find the inverse z-transform of $$x(z) = \dfrac {z^3 -4z^2 + 5z}{(z-1)(z-2)(z-3)}$$ (10 marks)

3 (a) What are the different types of the redundancies in image. (5 marks)

3 (b) Explain segmentation based on disontinuities. (5 marks)

3 (c) Define signals and system and also give the classification of discrete time signals with suitable example. (10 marks)

4 (a) Determine the system function and unit sample response of the given system described by the following difference equation. (Assume zero initial conditions).  y(n) = \dfrac {1}{4} y(n-2) + \dfrac {1}{2} y(n-1)+x(n). (10 marks)

4 (b) Check whether following sequence is periodic or not. If yes, find the fundamental time period.
x(n)=3 sin (0.01 πn) + 4 cos(10n).
(5 marks)

4 (c) Find auto-correlation of x(n)={1,2,3,2}. (5 marks)

5 (a) Perform histogram equalization on the given image transform.

 Gray level 0 1 2 3 4 5 6 7 No. of pixel 70 100 40 80 60 40 08 02
(10 marks)

5 (b) Obtain the digital negative and thresholding of following 8 bit per pixel image. T=150.

 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
(5 marks)

5 (c) Justify why Laplacian is not good edge detector. (5 marks)

6 (a) Construct imporved gray scale quantization code for the given level data set.
(100, 110, 124, 124, 130, 200, 210}.
(10 marks)

6 (b) Explain image restoration and its application. (10 marks)

### Write short notes on (any two):

7 (a) K.L. Transform. (10 marks)

7 (b) Wavelet transform. (10 marks)

7 (c) Trimmed average filter. (10 marks)

7 (d) Edge linking and boundary detection via graph theoritic techniques. (10 marks)

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