## Digital Signal Processing - Dec 2011

### 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.

### Justify/Contradict the following statements:-

**1(a)** If the energy of the signal is finite its power is zero.(5 marks)
**1(b)** Laplacian is better than gradient for detection of edges.(5 marks)
**1(c)** Walsh transform is nothing but sequence ordered Hadamard transform matrix.(5 marks)
**1(d)** All image compression technique are invertible.(5 marks)
**2(a)** Find the following sequence are periodic or not. If yes find the fundamental time period.

i)x_{1}(n)=e^{j(?/4)n}

ii) x_{2}(n)= 3 sin(1/8)n(10 marks)
**2(b)** Obtain linear convolution of two discrete time signals as below

x(n)=u(n)

h(n)=a^{n}u(n), a<1

Show that:

(10 marks)
**3(a)** Find the cross correlation between given signal.

(5 marks)
**3(b)** Find z-transformation of x(n) and draw its ROC

(10 marks)
**3(c)** Determine auto-correlation of following signal

(5 marks)
**4(a)** Using 4 point FET algorithm, calculate 2-D DFT of

(10 marks)
**4(b)** Write 8x8 Hadamard transform matrix and its single flow graph. Using butterfly diagram compute Hadamard Transform for x(n)={1,2,3,4,1,2,1,2}(10 marks)
**5(a)** Peform Histogram Equalization and draw new equalised histogram of the following imagedata.

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

i) Region Growing

ii) Region Splitting

iii) Thresholding(10 marks)
**6(a)** What are the different types of redundancies in digital image? Explain in detail.(10 marks)
**6(b)** For the 3 bit 4*4 size image perform following operation.

i) Threshold T=4

ii) Intensity level slicing with background r1=2 and r2=5

iii) Bit plane slicing for MSB and LSB planes

iv) Negation

(10 marks)

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

**7(a)** Discrete Cosine Transform(5 marks)
**7(b)** Wiener Filter(5 marks)
**7(c)** Difference between Low Pass and Median filter.(5 marks)
**7(d)** Hough Transform(5 marks)
**7(e)** Homomorphic filter(5 marks)
**7(f)** 4,8,m connectivity of image pixels(5 marks)