University of Mumbai 2008-5th Sem B.E Electrical and Electronics Engineering Signal Processing-I - Question Paper
Signal Processing-I Sem V June 2008
(3 Hours)
Question No. 1 Is compulsory.
N.B.(1)
(2)
(3)
W
1. %) (b)
(c)
Attempt any four questions out of remaining six questions.
Figures to the right indicate full marks.
Assumptions mad&hould b clearly stated ,
TC/c Sr
g CT/ r-*
Prove the BIBO stability conditionfor DTLTI system. *
Find Z-transform of periodic sequence : x(n){-1,4,-2, 6}
Determine wheather following signals are energy/power. Find its energy/power:
4xt+-
4
(i) x(t) = 3 cos
(*i> x(h) = (3)n u ( - n 1).
(d) Classify systems below for linearity/causality/time-invariance
(I) y(t) = [ 2 cos(t2) ] u(t) (ii) y(n) = x(2n)
(e) Express x(t) in terms of unit step functions and obtain Laplace Transform,
2. Difference equation of DTLTI system is :
-4 1 1
y(n) = *y y(n - 1) - - y(n - 2) + x(n) + - x(n - 1).
Find :
(i) Transfer function and impulse response of the system for stable case. 7
(ii) Realize the system using Direct form-ll 5
(iii) Find zero state and zero Input response if input applied, x(n) = (5)n u(n) and initial A conditions are y(- 1) = 1, y( - 2) = - 1.
10
3. (a) Compute fallowing intograie : s
<i) J sin 2t S(t-3) dt
w
J (4-t2) 5(t+3) dt
(iii) j t2 S(t-3)dt 0
(ii)
(b) Obtain linear convolution using circular convolution for x(n) = { 1, - 2. 2, 3 }, and h(n) = { - 1, 3, 1 }
10
5
15
[TURN OVER
Con. 2640-00-9946-08.
5. (a) Find DTFT of x(n) = {- 2, i, - 1 } and sketch Its magnitude ard phase plot.
2
10
10
(b) Find Fourier Transform of following signals
 |
+ b |
*
* &
uy
a*>to
*>b
-1
6. (a) Develop the block diagram and state variable model of the system
10
10
10
Y(s) 6
X(s) s3 + 6s2 +11s +6
(b) Convolve :
(i) x(t).8(t-t0)
(ii) S (t t,) *8 (t - lz ).
7. (a) The differential equation characterizing a CTLTI system is given by
at at
with initial conditions y( 0-) = - 1, y(0-*) = 1 Determine zero input and zero state response.
(b) Write short note on Power Density Spectrum of periodic signal.
(c) State and prove modulation property of Fourier Transform.
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| Earning: Approval pending. |
