2009 Kerala University B.Tech Electronics and Communications Engineering Fourth Semester B.Tech. Degree Examination, December 2009,03.404 : SIGNALS AND SYSTEMS (TA) Question paper

Fourth Semester B.Tech. Degree Examination, December 2009
(2003 Scheme)
03.404 : SIGNALS AND SYSTEMS (TA)
Time : 3 Hours Max. Marks : 100
PART – A
Answer all questions. (10×4=40 Marks)
1. Explain the Dirichlet conditions for FT representation.
2. Sketch the following signals.
a) r(–2t + 3) b) –anu(–n –1)
3. What is an eigen function ? What is its significance on LTI systems ?
4. Give the definitions for DTFS and CTFS.
5. Is x(t) = ?? ?? ????2
cos 2t ?? ??3 periodic ? If periodic, what is its period ?
6. Give four properties of the ROC of Z transform.
7. Derive the expression for convolution sum.
8. What do mean by BIBO stability ? State the conditions.
9. Prove the scaling property of delta function.
10. Prove that Magnitude spectrum of a real signal is an even function of frequency.

PART – B
Answer any two questions from each Module. (6×10=60 Marks)
MODULE – I
11. Graphically obtain the convolution of the following signals.
10
12. Obtain the FS representation of the following signal
10
13. A fixed linear system responds to the input x(t) = rect ?? ??
??
??
??
?? ??
2
t 1
with output
y(t) = (t + 1) exp(2t + 1) u(t + 1). Find the response to the input
2 rect ?? ??
??
??
??
?? ??
2
t 1
+ 3 rect ?? ??
??
??
??
?? ??
2
t 3
. 10
-3- 8078
MODULE – II
14. Find the Fourier Transform of the following signal.
10
15. An LTI system with impulse response h1(n) = u(n)
3
1 n
?? ??
??
?? ??
?? is connected in parallel
with another causal LTI system with impulse response h2(n). The resulting parallel
interconnection has frequency response
?? ?? ?? ??
?? ??
??
?? ??
?? ??
?? j j2
j
j
10 7e e
12 5e
H(e )
Determine h2(n). 10
16. Find the time domain signal whose DTFT is given below.
i) Magnitude of X(ej??)
ii) Phase of X(ej??)
10
MODULE – III
17. a) Prove the differentiation property of Laplace transform.
b) Determine the Magnitude of Fourier transform of the signal whose Laplace
transform is specified as 2
1
2
2
, Re(s)
s s 1
s s 1
X(s) ?? ??
?? ??
?? ?? ?? . 10
18. a) Make table comparing Laplace Transform and Z-transform.
b) Find inverse Z-transform of X(Z) using long division method
z 1
(z 1) (z 2)
z
x (z) ??
?? ??
?? . 10
19. a) Find inverse Laplace transform of x(s) ?? (2s ??1) (3s2 ??4s ??3) (s ??1) .
b) Write short notes on :
i) Unilateral Z-transform
ii) Relation between ZT and DTFT. 10
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