Chhattisgarh Swami Vivekanand Technical University 2007-4th Sem B.E Electronics
B. E. (Fourth Semester) Examination, Nov.-Dee,, 2007
(AEI, El, Et and T Engg. Branch) SIGNALS and SYSTEMS Time Allowed : Three hourx Maximum Marks : 80 Minimum Pass Marks : 28
Note : Part (a) of each unit is compulsory. Attempt any two parts frlm (b), (c) & (d). Answer should be brief and to the point. Unnecessary long anrer may result in loss of marks.
Unit-1
(a) Define linear time tsvzristf system.
(b) CSxek wbedaer the foikrwiag syscm is :
Q) Sftfr or &/a2tac
(u) Linear or non-linear
(iii) Causal or non-causal
(iv) Time invariant or time variant Given that:
(c) Skctcli Uk followiag signals unci calcubtc Jhcir energies: 7
(i) r **(/)
(ii) m(/)-u(/-I5)
(d) Give the graphical and mathematical representation of following sequences : 7
(i) Unit step sequence
(ii) Unit ramp sequence
(iii) Unit sample sequence
(iv) Exponential sequence
Uiiit>ll
2. (a) Define Fourier transform of a signal x (<). What is the condition for existence of Fourier transform of signal x (/). 2
\b) State and prove following properties of Fourier transform :
(0 Linearity
(ii) Tune shifting (Hi) Time scaling (e) For (he transfer function :
*+io
#(0
j*+Xr+2
Find tbe response (r)due to input x (j - sin hu<0
00 For the continuous time periodic sigrul
*(r) = 2+cosy/j+4sifty/j
determine the fundamental frequency ft, and fourier
*
series coefficient C such that x (0 ]L .
Uuit-lU
3. (a) Define State of a system.
(b) Find the stale spacc representation of the following
systera whose differential cquatioo representation is.
328415(28)
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