DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2012

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2012
KR-1068     [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.
1.	(a)	Periodic analog signal will be always remain periodic when converted into digital signal. Is it true and false? Justify your answer.	05
	(b)	Frequency domain representation of a periodic discrete time signal is a periodic. It is true or false? justify your answer.	05
	(c)	Obtain the pole-zero plot of casual symmetrical linear phase FIR filter with odd number of coefficients, assuming smallest length, if it is known to have zeros at z = j, z = 1, z = -1.	05
	(d)	A high pass linear phase FIR filter has a magnitude response -     | H(ejw) | = 4 sin(aw) - 3 sin(bw) Find values of 'a' and 'b' assuming minimum value of N. Obtain corresponding impulse response.	05
2.	(a)	Classify the following (i.c. (A), (B) and (C) ) as --   (i) Linear phase/Non-linear phase   (ii) FIR/IIR   (iii) All pass/high pass/low pass/band pass   (iv) Stable/unstable --            (A) H(ejw) = 3e-2jw            (B) H(Z) = z + 0.6/z - 0.8            (C) Given following pole-zero plot.	12
	(b)	Determine the zeros of the following FIR system and indicate whether the system is minimum phase, maximum phase or mixed phase.   (i) H(z) = 6 + z-1 + z2   (ii) H(z) = 1  z1 + 6z-2   (iii) H(z) = 1 - 5/2z-1 - 3/2z-2   (iv) H(z) = 1 - 5/6z-1 - 1/3z-2	08
3.	(a)	Design a casual digital high pass filter using windowing technique to meet the following specifications :-   Passband edge (ΩP) : 9.5 kHz Stoband edge : 2 kHz Stopband attenuation : > 40 dB Sampling frequency : 25 kHz	10
	(b)	Obtain the analog transfer function of a Butterworth low-pass filter with following specifications :-   Passband edge (ΩP) = 250 rad/sec. Passband attenuation < 0.1 dB Stopband edge (ΩS) = 2000 rad/sec. Stopband attenuation < 60 dB	10
4.	(a)	(i) If x(n) = { 1 + 2j, 3 + 4j, 5 + 6j, 7 + 8j}. Find DFT X(k) using DIFFFT.   (ii) Using the result obtained in (i) above not otherwise, find DFT of following        sequence :-           X1(n) = { 1, 3, 5, 7 } and           X1(n) = { 2, 4, 6, 8 }	10
	(b)	Obtain direct from I, direct form II realization to second order filter given by --      y(n) = 2 b cos(w0) y(n-1) - b2 y(n-2) + x(n) - b cos(w0) x(n-1)	10
5.	(a)	Using linear convolution find y(n) for the sequence -      x(n) = { 1, 2, -1, 2, 3, -2, -3, -1, 1, 2, -1} and h(n) = {1, 2} Compare the result by solving the problem using overlop and add method.	10
	(b)	Find the response of the difference equation given by -    y(n) = 5y(n-1) -6y(n-z) +-X(n) for x(n) = u(n).	10
6.	(a)	Explain up-sampling by an integer factor with neat diagram and waveforms.	10
	(b)	Why is the direct form FIR structure for the multirate system inefficient ? Explain with neat diagram. how this inefficiency is overcome in implementing a decimator and an interpolator.	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)	Comparison of FIR and IIR filters.