DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2014

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2014
MV-19989     [Total Marks : 100]
N.B. :	(1)	Question No. 1 is compulsory.
	(2)	Attempt any four questions out of remaining six questions.
	(3)	Assumptions made should be clearly stated.
	(4)	Figures to the right indicate full marks.
1.	(a)	Obtain a digital filter transfer function H(ω) by applying Imputse invariance transformation on the analog TF. Ha(s) = s/s2 + 3s + 2 Use fs = 1 K samples/sec.	05
	(b)	Consider a filter with TF :      H(z) = (z-1 - a) / (1 - az-1) Identify the type of filter and justify it.	05
	(c)	Find the number of complex multiplications and complex additions required to find DFT for 32 point sequence. Compare them with the number of computations required if FFT algorithm is used.	05
	(d)	Consider the sequence x(n) = δ(n) + 2δ(n - 2) + δ(n -3). Find DFT of x(n).	05
2.	(a)	A sequence is given as x(n) = {1 + 2j, 1 + 3j, 2 + 4j, 2 + 2j}      (i) Find X(k) using DIT-FFT algorithm.      (ii) Using the results in (i) and not otherwise find DFT of p(n) and q(n) where              p(n) = { 1, 1, 2, 2}              q(n) = { 2, 3, 4, 2}	06
	(b)	X(K) = +36, -4 + j9.656, -4 + j 1.656, -4, -4 -j 1.656, -4 -j4, -4 -j9.656 Find x(n) using IFFT algorithm (use DIT IFFT).	10
	(c)	Explain the properties of symmetricity and periodicity of phase factor.	04
3.	(a)	By means of FFT-IFFT method (DIT algo) Compute Circular convolution of      x(n) = {2, 1, 2, 1}     h(n) = {1, 2, 3, 4}	08
	(b)	An 8 point sequence x(n) = {1, 2, 3, 4, 5, 6, 7, 8}   (i) Find X(K) using DIF FFT algorithm (ii) Let x1(n) = {5, 6, 7, 8, 1, 2, 3, 4} Using appropriate DFT property and answer of previous part, determine  x1(K) (iii) Again use DFT property and find  X2(K) where  x2(n) = x(n) +  x1(n).	12
4.	(a)	Draw the Lattice filter realization for the all pole filter      H(z) = 1/1+3/4z-1 +1/2z-2 +1/4z-3	10
	(b)	Obtain DF-I, DF-II, cascade (First order sections) and parallel (First order sections) structures foe the system describe by      y(n) = -0.1 y( n -1) +0.72 y(n - 2) + 0.7 x(n) - 0.252 x(n -1).	10
5.	(a)	Design a  FIR low pass digital filter using Hamming window for N = 7  Hd(ejw) = e-3jω -0.75Π < ω < 0.75Π                 =0 0.75Π < | ω | < Π	10
	(b)	A LPF has following specifications :- 0.8 <  | H (ω | < 1 for   0 < ω < 0.2Π           | H(ω | < 0.2 for   0.6Π  < ω <  Π Find filter order and analog cut off frequency if   (i) Bilinear transformation is used for designing   (ii) Impulse invariance is used for designing	10
6.	(a)	Explain up sampling by an integer factor with neat diagram and waveforms.	10
	(b)	Explain the need of a low pass filter with a decimator and mathematically prove that ωy = ωxD.	10
7.	Write notes on any four of the following :-		20
	(a)	Frequency sampling realization of FIR filters
	(b)	Goertzel algorithm
	(c)	Set top box for digital TV reception
	(d)	Adaptive echo cancellation
	(e)	Filter banks.