DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2010

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December  2010
GT-8904     [Total Marks : 100]
N.B. :	(1)	Question No. 1 is compulsory.
	(2)	Attempt any four questions out of remaining six questions.
	(3)	Assume any data wherever required but justify the same.
	(4)	Figures to the right indicate full marks.
1.	(a)	A discrete time invariant and linear is describe by the difference equation -   y(n) = x(n) +2 x(n-1) +x(n-2) Obtain (i) Impulse response   (ii) Frequency response   (iii) Sketch magnitude and phase response   (iv) System response to the input (-)Π Π u(n).	10
	(b)	Explain the concept of decimation by integer (M) and interpolation by integer factor (L).	10
2.	(a)	Find DFT of the sequence using DIT FFT -      x[n] = { 1, -2, 2, 2, 1, 3, -3, 4, 5}	10
	(b)	Convert the analog filter with system function --       H(s) =      s+0.1 ___________ into a digital IIR filter using bilinear transformation. The digital filter should have a resonant frequency of w=Π/4 (S + 0.1)2 + 9	10
3.	(a)	A filter is to be designed with the following desired frequency response   Hd (ejw) = { 0         ; - Π/4 < w <  Π/4 (ejw))   ;  Π/4 < | W | <  Π/4 Determine the filter coefficients using Hamming window.	10
	(b)	Consider a casual LTI system which is defined by system function     H(s) =     1 + 1.4 Z-1 _____________________________ (1+1/2 Z-1 ) (1+1/2 Z-1 +1/4Z-2 )	10
	(c)	Obtain 01-I, DF-II, cascade and parallel realization structures.
4.	(a)	The frequency response of low pass filter is given by -   H (ejw) = { (ej3w)           ; - 0 < w < Π/2 0                  ;  Π/2 < | W | <  Π Realize the above filter using frequency sampling realization technique.	10
	(b)	Develop DIT FFT algorithm for N = 6 = 2.3 using split-radix method.	10
5.	(a)	The unit sample response of a system is h[n] = {3, 2, 1} use overlap-add method of linear filtering to determine output sequence for the repeating input sequence x [n] = {2, 0, -2, 0, 2, 1, 0, -2, -1, 0}	10
	(b)	Explain the subband coding of speech signal as an application of mutirate signal processing.	10
6.	(a)	Design a digital butterworth filter that satisfies the following constraint using bilinear transformation Assume T = 1 sec.   0.9 <  | H(ejw) | < 1 ; 0 < W < Π/2           | H(ejw) | < 0.2 ; 3 Π/4 < W <  Π	10
	(b)	Draw  pole-zero plot and sketch magnitude and phase response of finite impulse response fitter which is given by.       h[n] = (0.5)   ; 0 < n < 7	10
7.	Write short note on (any three)  :-		20
	(a)	Multistage approached to sampling rate conversion.
	(b)	Adaptive television echo cancellation.
	(c)	Goertzel Algorithm
	(d)	Digital resonator.