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x(t) = =e-*u(t) with the initial condition y(0) = —2

b) Consider and LTI system described by the differential equation (4)
‏د‎ +5y() = ‏و‎ ۳۲ = — 2x(t). Find the transfer function of the inverse

system and find out whether a stable and causal inverse system exists.

11 a) Using bilateral Laplace transform find the ROC of the signal x(t) = 072 fora) (6)

b>0 and b) b<0
b) For x(t) given below, plot x(—2t — 1) (4)
x(t)
4
|
3 1 a“
‏و‎
‎| ۱
1 1

PART (^
Answer any two full questions, each carries10 marks.

12 a) Find the exponential Fourier series and plot the magnitude and phase spectrum of (10)

the following waveform.

x(t)

22

13 9) Define sampling theorem. With the help of frequency spectrum explain signal (6)

reconstruction is possible only if sampling frequency is ‏گر‎ = 2f,,
b) Using Fourier transform property find the Fourier transform of (4)
x(t) = e“*u(t —2)
14 a) Using graphical method find the convolution of x[n] = (1,3,3,2] and (6)
h[n] = யனா u[n — 4]

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