## 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 |

** 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 (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)