## Digital Signal Processing - May 2013

### 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)** Explain signals and systems with help of suitable examples. Give applications of signals and systems.(5 marks)
**1 (b)** Find Z transform of the following finite duration signal and state its ROC :- X(n)={1,2,5,7,0,1}(5 marks)
**1 (c) ** Given X(n) = {0,1,2,3,}. Find x(k) using DIT-FFT Algorithm(5 marks)
**1 (d)** Find CONVOLUTION of following signals :-

X(n)={2,1,3,5} and h(n)={0,1,2,4}.(5 marks)
**2 (a)** Determine the system function and unit sample response of the system given by Difference equation :

Y(n)=1/2 Y(n-1) + 2 X(n)(10 marks)
**2 (b)** Perform Histogram Equalization for the following. Obtain a plot of original as well as Equalized Histogram.

Grey level | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

No. of Pixels | 100 | 90 | 50 | 20 | 0 | 0 | 0 | 0 |

**3 (a)**Given X(n) ={0,1,2,3,5,6,7} find X(k) using DIT-FFT algorithm.(10 marks)

**3 (b)**

Compute 2D DFT of given Image using DIT-FFT algorithm

$f(x,y)=\begin{bmatrix}
1 &2 &3 &2 \\\\4
&3 &2 &1 \\\\4
&3 &2 &4 \\\\3
&2 &1 &4
\end{bmatrix}$

**4 (a)**Explain in details Enhancement techniques in spatial domain used for images.(10 marks)

**4 (b)**What is HADAMARD Transform? Write a 4x4 Hadamard matrix and its applications.(10 marks)

**5 (a)**What is segmentation? Explain the different methods of image segmentation.(10 marks)

**5 (b)**Explain image Restoration and its applications.(10 marks)

**6 (a)** What do you understand by sampling and quantization with respect to Digital Image Processing? How will you convert an Analog image into a Digital Image?(10 marks)
**6 (b)** Name and explain different types of Data Redundancies associated with Digital Image.(10 marks)

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

**7 (a)** Wavelet Transform(10 marks)
**7 (b)** Properties of Fourier Transform(10 marks)
**7 (c) ** KL Transform(10 marks)
**7 (d)** Discrete Cosine Transform.(10 marks)