Signals And Systems Question Paper - May 17 - Electronics And Telecomm (Semester 4)

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Signals And Systems - May 17

Electronics And Telecomm (Semester 4)

Total marks: 80
Total time: 3 Hours INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.

a) What is cross correlation and auto correlation of the system.

(5 marks) 00

b) Determine the even and odd part of the following continuous time signals.

(5 marks) 00

x(t) = sin2t + cos 2t + sin t cos 2t
x(t) = $e^{-1}$ u(t)

c) Determine the laplace transform of the given signals:-

(5 marks) 00

d) Determine whether the given systems are linear or nor linear.

(5 marks) 00

y(t) = $x^2$ (t)
y(t) = $e^x$ (t)

e) Justify the following with fourier series,

(5 marks) 00

Odd functions only have sine terms and even function have no sine terms

a) Prove the following properties of Fourier series,

(10 marks) 00

Time shifting
Frequency scaling
Time Convolution
Time scaling

b) Determine the fourier series of the following signal shown:-

(10 marks) 00

a) Find the transfer function, impluse response and step response of a continous time LTI system, also sketch the impluse and step response.

(10 marks) 00

$\frac{dy(t)}{dt}$ + 2y(t) = 3x(t)

b) An LTI system is described by the equation:-

(10 marks) 00

y[n[ = x[n] + 0.8x[n-1] +0.8x[n-1] - 0.49y[n-2]

Determine the transfer function of the system. Skecth the poles & zeros of the z-plane.

a) Perform circular concolution of the two sequences by using tabular Array and by using Metrics method.

$x_2$[n] ={2,1,2,1} and $x_2$[n] = {1,2,3,4}

(10 marks) 00

b) Solve the difference equation for a given system using Z-transform.

(10 marks) 00

y[n] - 3y[n-1] - 4y[n-2] = x[n] + 2x[n-1]

a) Explain Gibbs phenomena, also explain the condition necessary for convergence for fourier series.

(5 marks) 00

b) Determine the power and energy of the following continuous time sigals:-

(5 marks) 00

x(t) = $e^{-2t}$ u(t)
x(t) = $e^{j(2t+\frac{\pi}{4})}$

c) Find the inverse Laplace tranform of :-

(10 marks) 00

X(S) = $\frac{4}{(S+2)(S+4)}$ if the ROC is

-2> Re{s} >4
Re {s} < -4
Re {s} > -2

a) Determine the inverse Z-tranform of the follwoing function:

(5+5 marks) 00

X(Z) = $\frac{1}{1-1.5Z^{-1} + 0.5Z^{-2}}$
X(Z) = $\frac{Z^2}{Z^2 - Z + 0.5}$

b) Detremine the convolution of the follwoing signals using Z-tranform,

(10 marks) 00

$x_1$[n] = n u[n]
$x_2$[n] = $2^n$ u [n-1]

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