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

Digital Signal and Image Processing (DSIP) Semester 7 (3 Hours) May 2009
VR-4737 [Total Marks : 100]
N.B:	(1)	Question no 1 is compulsory.
	(2)	Attempt any four questions from the remaining five.
	(3)	Make the necessary assumption wherever required.
1.	(a)	Derive the relationship between Z- transform, DTFT and DFT.	05
	(b)	Determine whether following signals are periodic (i) cos (0.3Πn + Π/6)         (ii) x(n) = sin (0.01 Πn)	05
	(c)	Find the step response of a system having difference equations       y(n) = x(n) - 0.4 y(n-1) + 0.05 y(n-2)	05
	(d)	Find the given system is linear phase or not prove your Answer :        h(n) = { 1, - 2, 0, 2 - 1}	05
2.	(a)	Using DIF-FFT find DFT of the following sequence       x(n) = { 1, 3, -2, 4, 1, 4, - 2, 3}	10
	(b)	Determine the frequency response, magnitude response, phase response of the system given by        y(n) - 1/2y (n - 1) = x(n) - x(n - 1).	10
3.	(a)	A low pass filter has desired response is given below :      Hd(eδw) = e-j3w      0 <  w < Π/2                       0           Π < W < Π Determine the filter coefficient h(n) for M = T using frequency sampling technique.	10
	(b)	Prove the following properties of DFT with example :      (i) Periodicity property      (ii) Convolution property.	10
4.	(a)	x(n) = δ(n) + δ(n - 1) - δ(n - 2) + δ(n - 3) + δ(n - 4) + δ(n - 5) h(n) = δ(n) + 2δ(n - 1) - δ(n - 2)      Find y(n) by linear convolution      Find y(n) by circular convolution.	10
	(b)	What are the conditions to be satisfied by LTZ system?	10
5.	(a)	Design a digital butterworth filter satisfying. The following constraints using bilinear transformation. Assume T = 1 sec.      0.9 < | H (ejw) | < 1     0 < w < Π/2               | H (ejw) | < 0.2   3 Π/4 <  Π	10
	(b)	For the direct form - II realization of IIR filter find :   (a) Transfer function of filter   (b) Corresponding difference equation   (c) Impulse response fraction of filter   (d) Pole zero pattern of filter   (e) State whether filter is stable or not.	10
6.	write short notes on any two :-		20
	(a)	Fetal ECG monitoring
	(b)	DSP processors
	(c)	Chirp-2 Algorithm