Digital Signal and Image Processing (DSIP) Semester 7 (3 Hours) December 2009

Digital Signal and Image Processing (DSIP) Semester 7 (3 Hours) December 2009
SP-6572 [Total Marks : 100]
N.B:	(1)	Question no 1 is compulsory.
	(2)	Attempt any four out of remaining six questions.
	(3)	Assume suitable data wherever necessary, justify the same.
1.	(a)	Find the even and odd parts of the signal x(n) = u(n).	05
	(b)	Determine whether following signals are periodic, if periodic detemine the fundamental period. (i) x(n) = Re {ejnπ1/2} + lm {ejnπ1/8}     (ii) x(n) = ejπ/6n cos (nπ/17)	05
	(c)	Determine the response of the relaxed system characterized by the impulse response h(n) = (1/2)2 u(n) to the input signal x(n) = 2n u(n).	05
	(d)	Find the natural response of the system described by the difference equation y(n) + 2y(n-1) + y(n-2) = x(n) + x(n-1) with initial condition y(-1) = y(-2) = 1.	05
2.	(a)	Define z-transform and explain the importance of ROC. State and prove initial value theorem and final value theorem.	10
	(b)	Find the z-transform of the following sequences : (i) x(n) = (1/2)n u(n+2) + (3)n u(-n-1)  (ii) x(n) = (1/3)n cos(nw0) u(n).	10
3.	(a)	Explain and draw the basic network structures for IIR system.	10
	(b)	A causal linear shift invariant system is characterized by the difference equation y(n) = 1/4 y(n-1) + 1/8 y(n-2) + x(n) - x(n-1). Find the system function, H(z) and the unit sample response, h(n).	10
4.	(a)	Compare between circular convolution and linear convolution. Determine the output response y(n) if h(n) = {1, 1, 1} : x(n) = {1, 2, 3, 1}by using :      (i) Linear convolution      (ii) Circular convolution      (iii) Circular convolution with zero padding.	12
	(b)	A linear phase FIR filter has H1(w) = cos w/2 + 1/2 cos 3w/2. Determine the impulse response h(n).	08
5.	(a)	Explain the decimation in time FFT and Decimation in frequency FFT. Draw the Butterfly Diagram for N = 8.	15
	(b)	State and prove parseval's Power relation and Energy Relation.	05
6.	(a)	Design a low pass Butterworth filter that has a 3-dB cut-off frequency of 1.5 KHz and attenuation of 49dB at 3 KHz.	10
	(b)	Explain the procedure to design Digital filters from Analog Filters using :   (i) Impulse invariance   (ii) Based on Differential Equation   (iii) Bilinear Transformation.	10
7.	Explain the following :-		20
	(a)	DSP Techniques Applied in Audit Signal Processing
	(b)	Different generations of Digital Signal processor
	(c)	Filter Design using Frequency Transformations
	(d)	Hilbert Transform relations for the DFT
	(e)	Chirp-z Transform Algorithms.