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

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2012
GN-6380     [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.
1.	(a)	Show that FIR filters are linear phase filters. Define group delay and phase delay.	08
	(b)	Find the response of the system given by difference equation y(n) - 5y(n-1) + 6y(n-2) = x(n) for i) x(n) = δ(n) and ii) x(n) = U(n)	06
	(c)	Draw Direct form and direct form -II realization of the system given by y(n)-3/4 y(n-1) + 1/8. y(n-2) =x(n) + 1/3.x(n-1)	06
2.	(a)	Derive Radix-2 Decimation in Time Fast Fourier Transform and draw its' signal flow graph	10
	(b)	Design FIR digital filter by using window method for the following specifications :-    H(ejw)= e-j3w -3Π/4  < ω < 3Π/4 | H(ejw) = 0 ; 3 Π/4 < |ω| <  Π Use hamming window of length = 7	10
3.	(a)	If      Hd( ω) = 1       for 0 < f < 800 Hz and |         Hd( ω) = 0       for f > 800 Hz. Given that sampling frequency Fs = 5000Hz Design FIR filter for length M = 5 using Bartiett window.	10
	(b)	Find 8-point FFT of x(n) = {1, 2, 2, 2, 1} using signal flow graph of Radix-2 Decimation in frequency FFT.	10
4.	(a)	Design a digital Butterworth filter satisfying the following constraints.   0.9 <  | H(ejw) | < 1 ; 0 < ω < Π/2           | H(ejw) | < 0.2 ; 3 Π/4 <ω <  Π With sampling period T = 1 sec, use Bilinear transformation method.	12
	(b)	State and  device Goertzel algorithm, also state its application.	08
5.	(a)	For the analog transfer function H(s) = 3/(s+2) (s+3) Determine H(z) with sampling period T = 0.1 sec using   (i) Impulse Invariant method   (ii) Bilinear Transformation method.	10
	(b)	Describe the application Goertzel algorithm in dual tone multi-frequency detection.	10
6.	(a)	With a suitable block diagram describe sub-band coding of speech signals.	10
	(b)	With a neat diagram describe frequency sampling realization of FIR filters.	10
7.	(a)	Explain up-sampling by non-integer factor, with a neat diagram and waveforms	10
	(b)	Explain the application of DTSP in adaptive echo cancellation.	05
	(c)	Describe the concept of digital resonator.	05