DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2013

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2013
LJ-13936     [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)	Transfer functions of casual and stable digital filters are given below. State whether these filters are Minimum . Maximum / Mixed Phased filters   (i) H1(Z) (1-1/2z)(1-1/4z) ________________ (Z-1/3)(Z-1/5) (ii) H2(Z) (1-1/2z)(1-1/4z) _________________ (Z-1/3)(Z-1/5) (iii) H3(Z) (1-1/2z)(1-1/4z) _________________ (Z-1/3)(Z-1/5)	20
	(b)	Compute DFT of the sequence X1,(n) = {1, 2, 3, 4} using property and not otherwise compute DFT of X2,(n) = {1+j, 2+2j, 4+4j, 2+2j}
	(c)	The impulse response of a system is h(n) = an u(n), a ≠ 0. Determine a and sketch pole zero plot for this system to act as :-   (i) Stable low pass filter.   (ii) Stable high pass filter.
	(d)	Draw direct form structure for a filter with transfer function, H(z) = 1 + 3z-1 +2z-3 + 4z-4
2.	(a)	Consider a filter with impulse response, h(n) = {0.5, 1, 0.5}. Sketch its amplitude spectrum. Find its response to the inputs   (i) X1(n) = cos (nΠ/2)   (ii) X2(n) = 3 + 2 δ (n) -4 cos (nΠ/2)	10
	(b)	Determine circular convolution of x(n) = {1,2,1,4} and h (n) = {1,2,3,2} using time domain convolution and radix-2FFT. Also find circular correlation using time domain correlation.	10
3.	(a)	Explain overlap and add method for long filtering. Using this method find output of a system with impulse response, h(n) = {1,1,1} and input x(n) = {1, 2, 3, 3, 4, 5}.	10
	(b)	Compute DFT of a sequence, x(n) = {1,2,2,2,1,0,0,0} using DIF-FFT algorithm. Sketch its magnitude spectrum.	10
4.	(a)	Draw lattice filter realization for a filter with the following transfer function. H(z) = 1/1 + 13/24Z-1 +5/8z-2 +1/3z-3	10
	(b)	Design a low pass Butter worth filter with order 4 and passband cut off frequency of 0.4Π. Sketch pole zero plot. Use Bilinear transformation. Draw direct form II structure for the designed filter.	10
5.	(a)	Design an FIR Bandpass filter with the following specifications :-      Length : 9      stop band cut off frequency : 0.7Π      Use Hanning window.	10
	(b)	The transfer function of a filter has two poles at z=0, two zeroes at z=-1 and a dc gain of 8. Final transfer function and impulse response. Is this a casual or noncasual filter? is this a linear phase filter? If another zero is added at z =-1 find transfer function and check whether it is a linear phase filter or not.	10
6.	(a)	Transfer function of an FIR filter is given by H(z) = 1-z-N Sketch pole zero plots for N = 4 and N = 5 Prove that it is a comb filter.	10
	(b)	Write about frequency sampling realizationof FIR filters.	10
7.	(a)	Explain the process of decimation for reducing sampling rate of signal.	10
	(b)	Compare various windows used for designing FIR filters.	10