M.Tech-M.Tech Embedded Systems Transforms and Probability for Electronics Engineering(Sathyabama University, Chennai, Tamil Nadu-2012)
Monday, 19 August 2013 07:09Duraimani
(Established under section 3 of UGC Act,1956)
Course & Branch :M.Tech - EMBED/VLSI/W-VLSI
Title of the Paper :Transforms and Probability for Electronics Engineering Max. Marks:80
Sub. Code :782101-SECX5016 (2008-2009-2010-2011)Time : 3 Hours
Date :26/05/2012 Session :FN
PART - A (6 x 5 = 30)
Answer ALL the Questions
1. A finite duration sequence of length L is given by determine the N point DFT of the sequence for N = L.
2. Determine the DFT of the sequence
3. Find the circular convolution of x1(n) and x2(n) by matrix multiplication method, given that x1(n) = {1,2,3,4,5} and x2(n) = {5,-4,3,-2,1}.
4. Compute the Harr transform of the 2x2 image
5. The Probability of a bomb hitting a target is 1/5. Two bombs are enough to destroy a bridge. If six bombs are aimed at the bridge find the probability that the bridge is destroyed.
6. If {N(t)} is a band limited white noise such that find the auto-correlation of {N(t)}.
PART – B (5 x 10 = 50)
Answer ALL the Questions
7. (a) Find the inverse DFT of x(k) = {1,2,3,4}.
(b) State and prove Parseval’s relation for the DFT.
(or)
8. Find the IDFT {X(k)} given that
X(k) = {4,3(1-i),2,3,(1+i)}, N = 4.
9. State and prove the following transforms
(a) Slant (b) Karhunen-Loeve transforms
(or)
10. (a) What is Hadamard transform? Construct Hadamard transform for n=3.
(b) Find the circular convolution of x(n) and y(n) by (i) Matrix multiplication method and (ii) Circular representation method if x(n) = {1,2,2,1} and y(n) = {2,1,1,2}.
11. (a) For the function f(t) = exp(-t/4)u(t) where u(t) is the unit step function, find the approximation fk (t) at resolution level k.
(b) Using the Mexican hat wavelet, derive a closed-form expression for the CWT of the function.
(or)
12. (a) Construct a biorthogonal perfect reconstruction filter bank with h(n) = {1/16, ¼, 3/8, ¼, 1/16} for n = -2, -1, 0, 1, 2 respectively.
(b) Compute the time-band width product for the Gaussian function.
13. (a) The probability of a man hitting a target ¼ (i) if he fires 7 times, what is the probability of his hitting the target atleast twice? (ii) How many times must he fire so that the probability of his hitting the target atleast once is greater than 2/3?
(b) State and Prove the properties of moment generating function.
(or)
14. (a) In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and variance of the distribution.
(b) Electric trains on a certain line run every half an hour between mid night and six in the morning. What is the probability that a man entering the station at a random time during this period will have to wait atleast minutes?
15. (a) A random process is defined as x(t)=A cost + B sin t where A and B are random variables with E(A)=E(B)= 0 and E(A2) = E(B2) and E(AB)=0. Prove that the process is mean ergodic.
(b) Derive the Auto correlation function of response.
(or)
16. (a) State and prove Wiener-Khintchine theorem for WSS random process.
(b) Consider a white Gaussian noise of zero and power spectral density applied to a low pass RC filter whose transfer function is Find the auto correlation function of the output random process.
| Earning: ₹ 5.10/- |
