MU Computer Engineering (Semester 7)
Digital Signal Processing
May 2015
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


Solve any five:
1 (a) Check unit step signal for energy power signal and find its value.
4 M
1 (b) Find DFT of x(n)={3,1,2,4} using DIF-FFT.
4 M
1 (c) Compare between lossy and lossless compression.
4 M
1 (d) Explain image fidelity criterion.
4 M
1 (e) Find Z.T. of \( x(n)= {2, \underset {\uparrow}{1}, 0, 3, 4} \) . Find ROC of x(z).
4 M
1 (f) Prove that 2D DFT matrix is an unitary matrix.
4 M

2 (a) Find the circular convolution of the two sequence.
5 M
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 M
2 (c) Find the inverse z-transform of \[ x(z) = \dfrac {z^3 -4z^2 + 5z}{(z-1)(z-2)(z-3)} \]
10 M

3 (a) What are the different types of the redundancies in image.
5 M
3 (b) Explain segmentation based on disontinuities.
5 M
3 (c) Define signals and system and also give the classification of discrete time signals with suitable example.
10 M

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

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

6 (a) Construct imporved gray scale quantization code for the given level data set.
(100, 110, 124, 124, 130, 200, 210}.
10 M
6 (b) Explain image restoration and its application.
10 M

Write short notes on (any two):
7 (a) K.L. Transform.
10 M
7 (b) Wavelet transform.
10 M
7 (c) Trimmed average filter.
10 M
7 (d) Edge linking and boundary detection via graph theoritic techniques.
10 M



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