DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2008

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2008
CO-3484 [Total Marks : 100]
N.B. :	(1)	Question No. 1 is compulsory.
	(2)	Solve any four questions out of remaining six questions.
	(3)	Assume suitable data if required.
1.	(a)	The analog signal x(t) is given below :   x(t) = 2 cos 2000 ∏t + 3 sin 6000 ∏t + 8 cos 12000 ∏t Calculate      (i) Nyquist sampling rate.      (ii) If the given x(t) is sampled at the rate Fs = 5000 Hz. What is the discrete           time signal obtained after sampling ?      (iii) What is the analog signal y(t) we can reconstruct from the samples if ideal              interpolation is used?	20
	(b)	Determine the casual and stable inverse of the system with impulse response          h(n) = δ(n)-1/2 δ(n-1).
	(c)	Suppose that H(z) and G(z) are rational and have minimum phase. Which of the following filters have minimum phase?      (i) H(z) G(z)      (ii) H(z) + G(z).
2.	(a)	Consider the digital filter shown in Figure :- (i) Determine the input-output relation and the impulse response h(n) (ii) Determine and sketch the magnitude | H (ω) | and the phase response ∠H(ω) of       the filter and find which frequencies are completely blocked by the filter. (iii) When ω0 = η/2, determine the output y(n) to the input      x(n) = 3 cos (η/3 n + 30o ) -∞< n <∞.	10
	(b)	For a continues time signal with equation, x(t) =sin [ 2 η 1000 t ] + 0.5 sin [ 2 η 2000 t ] sample the given signal at 8000 samples/esc find out 8 point DFT. Plot magnitude and phase response.	10
3.	(a)	Given x(n) = { 1, 2, 2, 1 }. Find corresponding DFT X(k) using DIT FFT.	10
	(b)	Explain Energy compaction capability of DCT.	10
4.	(a)	What is the linear phase filter? What conditions are to be satisfied by the impulse response of an FIR system in order to have a linear phase? Plot and justify compulsory zero locations for symmetric even antisymmetric even and antisymmetric odd FIR filters.	10
	(b)	Design the second order low pass digital Butterworth filter whose cut off frequency is 1 KHz at sampling frequency 104 samples per socond. (Use BLT method.)	10
5.	(a)	Design an FIR low pass digital filter with specifications --      Hd (ejω) = { e-j3ω  - 3Π/4 < ω < 3Π/4 0        3Π/4 < | ω | < Π	10
	(b)	A linear sfift-invariant system has a unit sample response given by             h(n) = { -0.01, 0.02, -0.10, 0.40, -0.10, 1.02, -0.01}      (i) Draw a signal flow graph for this system that requires the minimum number of          multiplications.      (ii) If the input to this system is bounded with I x(n) | < 1 for all n, what is the            maximum value that the output y(n) can attain?	08
	(c)	Define phase delay and group delay	02
6.	(a)	Implement the all pass filter using a lattice filter structure   H(z) = -0.512 + 0.64 z-1 -0.8z-2 + z-3 ---------------------------------------------------- 1-0.8z-1 + 0.64 z-2 - 0.512 z-3	08
	(b)	With the help of block diagram, explain architecture of TMS 32 C 5X series of processors.	08
	(c)	Compare impulse invariant and Bilinear transformation.	04
7.	Write short note on the following :-		20
	(a)	Filtering of long data dequences
	(b)	Goertzel Algorithm
	(c)	Frequency domain characteristics of the different types of window functions
	(d)	Coefficient quantization in IIR filters.