II/IV B.Tech Degree Examinations, January 2014
Second Semester
Signals and Systems
Time : 3 hours
Maximum Marks : 60
Answer question No.1 Compulsory
Answer ONE question from each Unit
1. Answer the following [12 x 1 = 12M]
a. Define Causality.
b. Give the expression for Exponential Fourier Series
c. What is Aliasing effect?
d. Define rise time.
e. Define Correlation.
f. What is white noise?
g. Give the expression for thermal noise generated in a resistor.
h. Differentiate between continuous and discrete random variable.
i. Define Joint distribution function.
j. Define Variance of a random variable.
k. Define Stability.
l. Give Dirchlet's conditions.
UNIT - I [1 x 12 = 12M]
2. A rectangular function f(t) is defined by f(t)=1 if 0<t<pi and -1 if pi<t<2pi. Approximate this function by a waveform 'sint' over the interval (0, 2pi) such that the mean square error is minimum.
2. b) Find the even and odd component of the signal
i) x(n)=3δ(n+2)+2δ(n+1)+δ(n)+4δ(n-1)+5δ(n-2)
ii) x(t)=sint+cost (OR)
3. a) Find the Fourier transform of Signum function.
3. b) State and prove time convolution and frequency convolution properties of Fourier transforms.
UNIT - II [1 x 12 = 12M]
4. a) The input voltage to an RC circuit is given as x(t)= te^{-3t}u(t) and the impulse response of this circuit is given by 2e^{-4t}u(t). Find the output y(t).
4. b) Verify Parseval's theorem for the energy signal x(t)= e^{-3t}u(t). (OR)
5. a) The system function of an LTI system is 1/(JW+2). Find the output of the system for an input (0.8)^{t}u(t).
5. b) Derive the conditions for distortion less transmission through a system.
UNIT - III [1 x 12 = 12M]
6. a) Write short notes on shot noise and thermal noise.
b) Derive the expression for noise figure of an amplifier. (OR)
7. a) Explain about equivalent noise band width.
7. b) The noise figure of a receiver is 20 dB and it is fed by a low noise amplifier which has a gain of 40 dB and noise temp of 80 K. Calculate the overall noise temp of the receiving system and the noise temperature of the receiver.
UNIT - IV [1 x 12 = 12M]
8. a) State and explain the properties of probability density function.
8. b) Find the cumulative distribution function of the Gaussian random variable. (OR)
9. a) Define random process and explain ensemble and sample function.
9. b) Explain power spectral density of random process. Explain its properties.