SIGNALS AND SYSTEMS PAPER 1

COMM. SIGNALS AND SYSTEMS EC 202 4th Sem May 2k5

Note: Section A is compulsory. Attempt any Four questions from Section B and any Two questions from section C.

Section A Marks: 2 each

1.
(a) Determine whether or not, the following signal is periodic
x(t) = 2 ej(t+?/2) u(t)
(b) What are random variables.
(c) Define mean Erogodicity.
(d) When is a random process said to be stationary?
(e) Write does the mathematical equation for Gaussian pdf?
(f) Define signal to noise ratio.
(g) Write down the units of noise figure.
(h) What is impulse response of a matched filter?
(i) Under what conditions an envelope detector fails to allow the envelope?
(j) Define transfer function of a system.

Section B Marks: 5 each

2. Prove time-shifting property of continuous-time Fourier series.

3. Explain Gaussian probability density function.

4. Let x(t) have the Fourier transform x(j w), and let p(t) be periodic with fundamental frequency wo and Fourier series representation:

Determine an expression for the Fourier transform of :
y(t) = x(t) .p(t)

5. Find the power spectral density function of:
x(t) = cos 10 ?t + cos 20 ?t
Also sketch the power spectral density function.

6. Discuss Ergodicity in detail.

Section C Marks: 10 each

7. Derive the mean and variance of the exponential distribution directly from the density without using the moment – generating function.

8. (a) Discuss envelope detector. Where does it find its application?
(b) Give the graphical interpretation of convolution theorem.

9 (a) Show that the effective noise temperature of n networks in cascade is given by:
Te=Te1+T e2/g1 + T e3/(g1 g2) +…….. T en/(g1 g2………gn-1)
(b) What do you mean by noise figure? How do we determine it experimentally?