DS4152 Statistical Signal Processing Syllabus:
DS4152 Statistical Signal Processing Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
To introduce the basics of random signal processing
To learn the concept of estimation and signal modeling
To know about optimum filters and adaptive filtering and its applications
UNIT I DISCRETE RANDOM SIGNAL PROCESSING
Discrete random processes – Ensemble averages – Wide sense stationary process – Properties – Ergodic process – Sample mean & variance – Auto-correlation and Auto-correlation matrices- Auto covariance and Cross covariance- Properties – White noise process – Wiener Khintchine relation – Power spectral density – Filtering random process – Spectral Factorization Theorem – Special types of Random Processes – AR,MA, ARMA Processes – Yule-Walker equations.
UNIT II PARAMETER ESTIMATION THEORY
Principle of estimation and applications-Properties of estimates-unbiased and consistent estimators, Minimum Variance Unbiased Estimates (MVUE)-Cramer Rao bound- Efficient estimators; Criteria of estimation: Methods of maximum likelihood and its properties ; Bayesian estimation : Mean square error and MMSE, Mean Absolute error, Hit and Miss cost function and MAP estimation
UNIT III SPECTRUM ESTIMATION
Estimation of spectra from finite duration signals, Bias and Consistency of estimators – Non Parametric methods: Periodogram, Modified Periodogram, Bartlett, Welch and Blackman-Tukey methods, Parametric Methods: AR, MA and ARMA spectrum estimation – Detection of Harmonic signals – Performance analysis of estimators. MUSIC and ESPRIT algorithms
UNIT IV SIGNAL MODELING AND OPTIMUM FILTERS
Introduction- Least square method – Pade approximation – Prony’s method – Levinson Recursion – Lattice filter – FIR Wiener filter – Filtering – Linear Prediction – Non Causal and Causal IIR Wiener Filter -– MSE – State-space model and the optimal state estimation problem, discrete Kalman filter, continuous-time Kalman filter, extended Kalman filter.
UNIT V ADAPTIVE FILTERS
FIR Adaptive filters – Newton’s steepest descent method – Widrow Hoff LMS Adaptive algorithm – Convergence – Normalized LMS – Applications: Noise cancellation, channel equalization, echo canceller, Adaptive Recursive Filters: RLS adaptive algorithm, Exponentially weighted RLS-sliding window RLS. Matrix inversion Lemma, Initialization, tracking of nonstationarity.
COURSE OUTCOMES:
On the successful completion of the course, students will be able to
CO1: Analyze discrete time random processes
CO2: Apply appropriate model for estimation and signal modeling for the given problem
CO3: Analyze non-parametric and parametric methods for spectral estimation
CO4: Design optimum filter for the given problem
CO5: Design adaptive filters for different applications
TOTAL:45 PERIODS
REFERENCES:
1. Monson. H. Hayes, Statistical Digital Signal Processing and Modelling, John Willey and Sons, 1996 (Reprint 2008)
2. Simon Haykin, Adaptive Filter Theory, Pearson Prentice Hall, 5th edition, 2014
3. D.G. Manolakis, V.K. Ingle and S.M. Kogon, Statistical and Adaptive SignalProcessing, Artech House Publishers, 2005.
4. Steven. M. Kay, Modern Spectral Estimation, Theory and Application, Pearson India, 2009
5. A.Veloni, N I. Miridakis, E Boukouvala, Digital and Statistical SignalProcessing, CRC Press, 2019
6. S Nandi, D Kundu, Statistical Signal Processing- Frequency Estimation, Springer Nature Singapore, 2ndedition , 2020
7. M.D. Srinath, P.K. Rajasekaran and R. Viswanathan, Statistical Signal Processing with Applications, PHI, 1996.