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  • 3:16 PM, Sunday, 26 Sep 2021

Department of Avionics
Lakshmi Narayanan R., Ph.D.
Assistant Professor

  • Ph.D from the Department of Electrical Engineering, IITM. The doctoral work focuses on the large scale error sensitivity analysis of the Kalman filter and the H-infinity estimator.
  • M.E from Anna University in Applied Electronics.

  • Worked as a project officer at IITM for an year from 2009-2010, on developing algorithms for Channel estimation problems in an OFDM based communications systems.
  • Worked with TATA ELXSI as communications specialist from October 2010  to November 2011.

Prerequisites : Signals and Systems (AV311)

The following topics will be covered in this course :

  • The Z-Transform
  • Conversion of Analog Signals into Discrete time Signals
  • Transform Domain Analysis of LTI Systems
  • Discrete time Fourier Series and Transform
  • Design of Digital Filters


Textbook : Discrete Time Signal Processing (3rd Edition),

Authors : Allen Oppenheim and Schafer



Prerequisites : Probability and Random Processes, Linear Algebra

Topics Covered : In this course we cover topics from Estimation and Detection Theory

  • Estimation Theory
  1. Minimum Variance Unbiased Estimation
  2. Maximum Likelihood Estimation
  3. Sufficient Statistics and Factorization Theorems
  4. Cramer rao Lower Bound
  5. Properties of Estimators
  6. Least Squares Estimator
  7. Best Linear Unbiased Estimator
  8. Method of Moments
  9. Bayesian Estimation - Maximum a Posteriori, Minimum Absolute Deviation, Minimum Mean Squared Error Estimators
  10. Wiener Filter - FIR/IIR
  11. Kalman Filter
  • Detection Theory
  1. Statistical Hypothesis Testing
  2. Minimum Probability of Error

This course primarily concentrates on Probability and Random Processes. The course contents are,

  1. Set Theory and Basic Axioms of Probability
  2. Conditional Probability and Independence
  3. Random Variables - Discrete and Continuous
  4. Cumulative Distribution Function (CDF), Probability Density Function (PDF)
  5. Moments of a Distribution
  6. Multiple Random Variables
  7. Conditional Density Function, Marginal Densities
  8. Some useful Density Functions
  9. Transformation of Random variables
  10. Characteristic Function
  11. Moment Generation Function
  12. Sums of Random Variables
  13. Law of Large Numbers - Weak and Strong Law,
  14. Central Limit Theorem
  15. Random Processes - Stationary, Non-stationary, Wide-Sense Stationary
  16. Filtering Random Processes
  17. Auto-correlation/Cross-Correlation Functions and Power Spectral Density of Random Proecsses
  18. White Noise, gaussian and Poisson Random processes
  19. Properties of Correlation Functions and Power Spectral Density.


Texts and References :

1. Probability and Stochastic Processes, Author : Papoulis, Unni Krishna Pillai


  1. Introductions to Signals and Systems - Basic Types and Basic Operations
  2. Interactions of signals with Linear Time Invatiant (LTI) systems - Convolution operation
  3. Periodic Signals - Fourier Series Expansion and its peroperties
  4. Aperiodic Systems - Fourier Transformation and its properties
  5. Generalized Fourier Transform
  6. Approximations on a Vector Space
  7. Laplace Transform
  8. Sampling of Continuous Time Signal - Nyquist criterion for lossless reconstruction
  9. z- Transform



Texts and References :

1. Signals and Systems by Allen Oppenheim, Willsky

2. Linear Systems and Systems by B. P Lathi

3. Signals and Systems by Simon Haykin