R09 Code No: D4502

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD M.Tech II Semester Examinations, October/November 2011

ADAPTIVE SIGNAL PROCESSING (SYSTEMS & SIGNAL PROCESSING)

Time: 3hours Max. Marks: 60 Answer any five questions

All questions carry equal marks - - -

1.a) Give the block diagram of an adaptive system and explain the principle of adaptation

in detail there by give the application of the system for real time analysis. b) Define Autocorrelation Matrix and bring out its importance in signal analysis. Prove the following Properties

i) The correlation matrix of a stationary discrete time stochastic process is Hermitian. ii) The correlation matrix of a wide sense stationary process is non-singular due to the unavoidable presence of additive noise. [12]

2.a) State Wiener-Hopf equation and derive the expression to calculate optimum weights

in terms of correlation matrix R and cross-correlation vector P. b) For the given data R and P Evaluate the tap weights and also calculate MMSE

produced by the wiener filter. [12] 1 0.5 0.25 R = 0.5 1 0.5 and P = [0.5 0.25 0.125] T 0.25 0.5 1 3.a) Explain Steepest descent algorithm and derive the iterative equation to calculate the

tap weights b) Explain the role of step size parameter in achieving stability in steepest descent and derive the necessary condition. [12] 4.a) Explain the Principle and Operation of LMS algorithm. b) Discuss in brief how the LMS adaptation algorithm differs from steepest gradient algorithm. [12] 5.a) Explain the principle of operation of Adaptive Echo Cancellation.

b) Show that the optimum weights can be computed in a single iteration using Newtons Algorithm. [12]

6.a) Explain the Kalman filter problem statement and discuss its operation. b) Define Innovation process and explain the properties of it. [12] 7. Write short notes on the following w.r.to Kalman Filter a) Divergence Phenomenon

b) UD Factorization c) Square root filtering. [12]

8.a) Derive an expression for the cost function J and show that the estimation error e(n) is

orthogonal to the input U(n) when J attains Minimum value. b) Derive an expression to calculate the Minimum mean square error. [12]

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