II/IV B.Tech Degree Examinations, June 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) State the sampling theorem.
b) What is the condition for Causality in terms of impulse response for a LTI system?
c) Give the equation for Trigonometric Fourier Series.
d) What are the Dirichlet's conditions of Fourier series?
e) What is anti- aliasing filter?
f) What is Linear filtering?
g) What is a Random process?
h) What is Noise equivalent bandwidth?
i) What is the effect of filtering on Noise bandwidth?
j) Define Probability density function.
k) Give the expression for PDF of a Gaussian variable.
l) Define ergodicity of a process.
UNIT - I [1 x 12 = 12M]
2. a) Determine the exponential Fourier series for an impulse train. Also plot its magnitude and phase spectrum.
2. b) Find the Fourier transform of 5 sin^{2}(t). (OR)
3. a) State and prove any three properties of the continuous-time Fourier transform.
3. b) Find the Fourier series coefficients of the signal x(n)=sinω_{0}n and plot them.
UNIT - II [1 x 12 = 12M]
4. a) Explain Parseval's relation for discrete time periodic signals.
4. b) Find the convolution of the signals x(t)= e^{3t}u(-t) and h(t)=u(t-10) and plot x(t) ,h(t) and x(t)*h(t). (OR)
5. a) Define Energy Spectral density. State and prove its properties.
5. b) Derive the condition for stability in terms of impulse response for a LTI system.
UNIT - III [1 x 12 = 12M]
6. a) Derive the expression for the overall noise figure of a cascaded amplifier with two stages.
6. b) Derive the equations for power spectral density of n_{c}(t) and n_{s}(t). (OR)
7. a) Write short notes on "Thermal Noise".
7. b) Two resistors of 10 K Ohms and 5 K Ohms at room temperature 30^{o}C are used for a communication system operated at B.W of 100 K Hz. Calculate the thermal noise generated by each resistor when connected in series, in parallel.
UNIT - IV [1 x 12 = 12M]
8. a) Discuss in detail stationarity of random process.
8. b) Evaluate the power density spectrum of the response of a linear time invariant system when excited by a random process X(t). (OR)
9. a) Discuss the auto correlation properties of a random process.
9. b) Discuss about ergodic random process.