Digital Signal Processing - May 2014

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) Laplacian is not good edge detector. Justify.(5 marks) 1 (b) Discuss the properties of Region of Convergence.(5 marks) 1 (c) Convolution in one domain leads to multiplication in other domain.(5 marks) 1 (d) Walsh transform is nothing but sequence Orderd Hadamard Transform Matrix Justify.(5 marks) 2 (a) Construct following gray scale quantization code for given level data set.
{100, 110, 124, 130, 200, 210}(10 marks) 2 (b) Find the following sequence are periodic or no. If yes, find the fundamental time period-
(i) x₁(n)=3sin(0.01 ?n)+4cos(10 n)
(ii) x₂=cos(0.01 ?n)
(10 marks) 3 (a) Determine the system function and unit sample response of the given system described by following difference equations :
$$y(n)= \frac{1}{4} y(n-2)+\frac{1}{2}y(n-1)+x(n)$$(10 marks) 3 (b) Find cross-correlation between given signals.
x(n)={1,0,1,2}
y(n)={1,2,3,4}
(5 marks) 3 (c) Find auto-correlation of following signal
x(n)={1,1,2,3}(5 marks) 4 (a) Compute DFT of the given image using DIF-FFT technique

Write short noes on (any four) :-

7 (a) Hough transform(5 marks) 7 (b) Wavelet Transform(5 marks) 7 (c) Classify and define discrete time systems(5 marks) 7 (d) Homomorphic filtering.(5 marks) 7 (e) State and prove convolution property of Z-transform.(5 marks)