DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2009

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2009
SP-6635     [Total Marks : 100]
N.B. :	(1)	Question No. 1 is compulsory.
	(2)	Attempt any four questions out of remaining six questions.
	(3)	Assume suitable data if required.
1.	(a)	Determine the coefficients {h(n)} of a highpass linear phase FIR filter of length M = 4 which an ant symmetric unit sample response h(n) and a frequency response that satisfies the condition   | H (Π/4) | =1/2, | H (3Π/4) | = 1	20
	(b)	Obtain the mapping formula for the bilinear transformation method.
	(c)	How may we compute the N-point DFT of two real valued sequence, x1(n) and x2(n) using one N-point DFT?
	(d)	Compare Analog and Digital filters.
2.	(a)	Justify that the spectrum of an aperiodic discrete time signal with finite duration L, can be recovered from its samples at frequencies ωk = 2 Π k/N, if N>L. Where N is the number of frequency samples in frequency domain and k=0,1,2,....., N-1	08
	(b)	Design a digital resonator with a peak gain of unity at 50 Hz and 3dB bandwidth of 6Hz assuming a sampling frequency of 300Hz.	06
	(c)	Realize a coupled form oscillator ( two sinusoidal carrier signals in phase quadrate) with the help of block diagram.	06
3.	(a)	Find DFT of   (i) x(N) = {1, 1, 1, 1} 04 (ii) x(N) = {1, 0, 1, 0, 1, 0, 1, 0} 03 (iii) x(N) = {1, 1, 1, 1, 1, 1, 1, 1} 03
	(b)	Explain the Frequency Sampling method of designing an FIR filter.	10
4.	(a)	What is DCT? Explain how DCT is classified in four types as DCT-I, DCT-II, DCT-III and DCT-IV. Which type is mostly used and why?	10
	(b)	Design a digital Butterworth filter to satisfy the constraints,   √0.5 < | H (ejw)| < 1. 0 < ω < Π/2 | H (ejw)| < 0.2. 3Π/4 < ω < Π	10
5.	(a)	Given x(n) = n+1 and N=8 Find DFT X(k), using DIF FFT algorithm.	10
	(b)	Obtain the direct form-1 and direct form-II realization for the second order filter given by y(n) = 2b cosω0y(n-1) - b2y(n- 2) + x(n) - b cosω0x(n-1)	10
6.	(a)	Design low pass FIR filter to satisfy following specifications   Hd(ejw) = {    e-j2w, Π/4 < ω <  Π/4 Π/4 < ω < Π Determine the filter coefficients hd(n) if the window function is defined as   W(n) = {    1, 0 <  n < 4 0, otherwise Also determine the frequency response Hd(ejw) of the designed filter.	10
	(b)	Compare the DSP processors and general purpose processors.	10
7.	Write short note on the following :-		20
	(a)	TMS 32 C 5 X series of processors
	(b)	Finite word length effects in digital filters
	(c)	Applications of DCT.