DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) may 2010

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) may 2010
AN-2854     [Total Marks : 100]
N.B. :	(1)	Question No. 1 is compulsory.
	(2)	Attempt any four questions out of remaining six questions.
	(3)	Assume any data wherever required but justify the same.
	(4)	Figures to the right indicate full marks.
1.	(a)	Sketch the pole-zero plot for the system with transfer functions   H(z) = Z6 - 26 if the system is stable. Z5 - (Z - 2)	05
	(b)	One of the zeros of a casual linear phase FIR filter is at 0.5 ej Π/3. Show the locations of the other zeros and hence find the transfer function and impulse response of the filter.	05
	(c)	Derive the relationship between DFT and DCT.	05
	(d)	Find the convolution of the following signals and system transfer function using Z-transform. X[n] = δ[n] + δ[n - 1] and h[n] = (1/2)n u(n).	05
2.	(a)	Using DIF FFT find DFT of following dequence       x[n] = {1, 3, - 2, 4, 1, - 2, + 3}	10
	(b)	, (i) Using results in Q2(a) find X2(k) if       X2[n] = x[n -2] 05 (ii) Using results in Q2(a) find X3(k) if       X3[n] = x*[n] 05
3.	(a)	Design a digital Butterworth low pass filter satisfying the following specifications using bilinear transformation (Assume T = 1 sec)   0.9 <  | H(ejw) | < 1 ; 0 < W < Π/2           | H(ejw) | < 0.2 ; 3 Π/4 < W <  Π	10
	(b)	Derive and draw the FFT  for N = 6 = 2.3 using DIT FFT method.	10
4.	(a)	Determine the filter coefficients h[n] for the desired frequency response of a low pass filter.   Hd (ejw) = { e-j2w ; - Π/4 < w <  Π/4 0      ;  Π/4 < | W | <  Π use Hamming window.	10
	(b)	The difference equation of the system is given by :      y[n] = 3y[ n-2] + 2y[n-1] + x[n] and      x[n] = (1/2)n u[n] with y(-1) =y(-2) = 1 Determine :    (i) Zero input response    (ii) Zero state response    (iii) Total response.	10
5.	(a)	For direct form-II realization of IIR filter, find :   (i) Transfer function of the filter (ii) Difference equation (iii) Impulse response of the filter (iv) Step response of the filter (v) Pole-zero plot of the filter (vi) State whether filter is stable or not and why?	12
	(b)	Convert the analog filter into digital filter by using impulse invariance transformation method.             Ha(s) = s+0.4/(s+0.4)2 + 9	08
6.	(a)	With the help of block diagram, explain TMS 320 (5x series of processors).	10
	(b)	Design a digital resonator with a peak gain of unit at 50 Hz and 3 dB bandwidth  of 6 Hz assuming a sampling frequency of 300 Hz.	10
7.	Write short note on the following :-		20
	(a)	Filtering of long data sequences
	(b)	Geortzel Algorithm
	(c)	Frequency wrapping
	(d)	Coefficient Quantization in IIR filter.