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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
M.E. SEMESTER II-EXAMINATION -2016-17
Subject code: 2720505 Date:29/05/2017
Subject Name: Adaptive Signal Processing
Time: 02:30 p.m.-5:00 p.m. Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Derive the principle of orthogonality for a statistical filtering problem. Derive Wiener-Hopf equations from it. Also derive the solution of the Wiener-Hopf equations for linear transversal filters in matrix form.
07

Derive the weight update formula for LMS algorithm. Discuss about its complexity. Derive the weight update formula if LMS algorithm is to be applied when is not given but the correlation function between and is given.
07
Q.2

Consider an autoregressive process of order 2 described by the difference equation
where is white noise with zero mean and variance 0.5.
Find the variance of
Write the Yule-Walker equations for the process.
Solve these two equations for the autocorrelation function values and
Find the correlation matrix, eigenvalues, unit eigenvectors, eigenvalue spread and minimum mean square error.
07

i Write the properties of the correlation matrix Prove that the
correlation matrix of a discrete-time stochastic process is always
non-negative definite.
ii Explain the terms: eigenvalue spread, misadjustment, smoothing,
gradient noise.
05
02
OR

Derive augmented Wiener-Hopf equations for forward prediction and use them to find the weights and power of forward prediction-error filter of order .
07
Q.3

i Explain the basic idea of the steepest descent algorithm and show
that the cost function is actually minimized if the weights are
updated according to the formula obtained.
ii State the Levinson-Durbin algorithm.
05
02

Draw the signal flow graph representation of the steepest descent algorithm. Discuss Newton's method. Compare the method of steepest descent and Newton's method.
07
OR
Q.3

i Describe the four classes of applications of adaptive filtering.
ii Explain the three basic kinds of estimation.
05
02

i Mention some of the criteria to evaluate the performance of a
recursive algorithm for adaptive filtering.
ii Write the properties of prediction-error filters
05
02
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Q.4

Deduce Fast Block LMS Algorithm and show that it is actually faster than LMS Algorithm in computational terms.
07

Write a short note: RLS Algorithm
07
OR
Q.4

In the context of Kalman Filtering, draw the signal-flow graph representation of a linear, discrete-time dynamical system. What is transition matrix? Write properties of transition matrix. Also write the process equation and measurement equation.
07

Derive the weight update formula for the Normalized LMS Filter as the solution to a constrained optimization problem.
07
Q.5

What is the advantage of using an IIR filter instead of an FIR filter? Describe output error method for designing an IIR adaptive filter.
07

Explain how adaptive signal processing is useful to enhance signal reception quality with an array of antennas.
07
OR
Q.5

Describe in detail: Hum removal of an ECG signal using adaptive signal processing.
07

Explain how the problems of multipath for troposcatter signals can be tackled using adaptive signal processing.
07