EC6303 Signals and Systems, Second year, Department of Electronics & Communication Engineering, First and second Units Questions

PART A – (10 x 2 = 20 Marks)
1.      Define energy and power signal.
2.      Determine the laplace transform of the signal δ(t-5).
3.      Define random signal.
4.      Give the mathematical and graphical representation of continuous time and discrete time unit impulse function.
5.      Verify whether the system described by the equation is linear y(t)=x(t2)
6.      Find the fundamental period of the given signal x (n) =sin ((6Ï€n/7+1)).
7.      Distinguish between fourier series and fourier transform.
8.      State Dirichlet condition.
9.      Prove the time shifting property of discrete time fourier transform.
10.  Determine laplace transform of x(t)=e-atsinwtu(t)
                                             PART B-(5x13=65Marks)
1.       Determine whether the systems described by the following input-output equations are
linear,dynamic,causaland time variant.
i)y1 (t)=x(t-3)+(3-t)
ii)y2(t)=dx(t)/dt
iii) y1(n)=n x(n)+bx2(n) (13)   
2.      i)Determine whether the signal x(t)=sin2Ï€t+sin5Ï€t is periodic and if it is periodic find
the fundamental period.                                              (5)
ii)Define energy and power signals. Find whether the signal x (n) = (1/2) nu (n) is
energy or power signal and calculate their energy or power.  (5)
iii) Discuss various forms of complex exponential signals with graphical
representation.(3)


3.      i) Prove the scaling and time shifting properties of laplace transform.(6)
ii)Determine the laplace transform of x(t)=e-atcoswt u(t)                                            (7)

4.      Determine the fourier series representation of the half wave rectifier output shown
in  figure below.
                                            (13)
5.      Determine the complex exponential fourier series for periodic rectangular pulse train
shown in figure.plot its magnitude and phase spectrum.                                      (13)
PART C-(1x15=15Marks)
1.Write brief notes about Road TrafficSignal Systems.                                              (15)