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  • 3:11 AM, Saturday, 20 Apr 2024

Department of Avionics
     
Lakshminarayanan R., Ph.D.
Associate Professor
 
Office
Tel:0471-2568580
Fax:
Email:lakshminarayanan@iist.ac.in













Education
  • 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.

Course Offered

Masters Courses

  1. Statistical Signal Processing
  2. Mathematical Methods and Algorithms for Signal Processing
  3. Information Theory and Error Control Coding
  4. DSP for Digital Communication
  5. Advanced Digital Signal Processing
 
Bachelors Courses
  1. Digital Signal Processing
  2. Signals and Systems 
  3. Digital Communication
  4. Information Theory and Error Control Coding
  5. Stochastic Processes and Estimation Theory
  6. Microprocessors and Microcontrollers
  7. Radar Systems (The Signal Processing part)

Experience
  • Associate Professor (February 2006 - Till date), Department of Avionics, Indian Institute of Space Science and Technology, Thiruvananthapuram, India.
  • Assistant Professor (November 2011 - January 2016), Department of Avionics, Indian Institute of Space Science and Technology, Thiruvananthapuram, India.
  • Worked with TATA ELXSI as communications specialist from October 2010  to November 2011.
  • Research Associate (2009-2010), TeNet (Telecom and Networking) group, Indian Institute of Technology Madras, Chennai, India.
  • Teaching Assistant (2002-2009), Systems and Control Engineering, Indian Institute of Technology Madras, Chennai, India.

Research Work / Area

I primarily work in the area of statistical signal processing with applications to communications.

  1. Thorough study and comparison of  the MSE performance of Kalman filter and the H-Infinity Estimator in the presence of statistical uncertainties.
  2. Presently working on Compressed Sensing. 
  3. Radar Signal processing for detection of micro-drones. 
  4. On certain phase prediction for free space optical communication.

Teaching Interest
 
  1. Machine Learning
  2. Pattern Recognition
  3. Certain Advanced topics in Digital Signal Processing
  4. Data Anaytics
  5. Time Series Analysis

 

 

Prerequisites : Signals and Systems (AV311)

The following topics will be covered in this course :

  1. Review of Signals and Systems
  2. The Z-Transform
  3. Conversion of Analog Signals into Discrete time Signals and Sampling Theorem
  4. Upsampling, downsampling and Sampling Rate Conversion
  5. Transform Domain Analysis of LTI Systems
  6. Discrete time Fourier Series and Transform
  7. Design of Digital Filters - FIR and IIR
  8. Selected topics on Applications of DSP 

Textbook :

  • Discrete Time Signal Processing (3rd Edition) - Allen Oppenheim and Schafer
  • Digital Signal Processing, Principles, Algorithms and Applications - John G Proakis, Dimitris G Manolakis

Prerequisites : Probability and Random Processes, Linear Algebra

Topics Covered : In this course we cover topics from Estimation and Detection Theory or statistical Inferencing. Essentially it deals with problems of (i) determining the values (estimating) of some random or deterministic quantity in the presence of noise and (ii) making inferences about the a desired parameter based on certain measurements. 

  • 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 
  11. Kalman Filter
  • Detection Theory
  1. Statistical Hypothesis Testing
  2. Minimum Probability of Error 
  3. Maximum A Posteriori Detector
  4. Bayesian Detector
  5. Neyman-Pearson Detector, Receiver Operating Characteristic
  6. Composite Hypothesis Testing
  7. The General Gaussian Problem
  8. Detection of Known Signals in white Gaussian Noise
  9. Detection of Known Signals in non-Gaussian Noise
  10. The Karhunen-Loeve Expansion
  11. Generalized Likelihood Ratio Test

 

An exhaustive list of books on Statistical Signal Processing is as given below. Students may choose books from the following according to their preferences (style of writing etc)

  • Text Books
  1. Fundamentals of Statistical Signal Processing - Vol1, Estimation Theory - Steven Kay
  2. Fundamentals of Statistical Signal Processing - Vol1, Detection Theory - Steven Kay
  3. Discrete Random Signals and Statistical Signal Processing - Charles W. Therrien
  4. Statistical Signal Processing and Modeling - Monson Hayes
  5. Lessons in Digital Estimation - Jerry K Mendel
  6. Detection, Estimation and Modulation Theory - Volume 1, Van der Veen
  7. Optimum Signal Processing - Sophocles J. Orfanidis. This book can be downloaded from the author's website http://eceweb1.rutgers.edu/~orfanidi/osp2e/osp2e.pdf

 

This course primarily concentrates on Probability and Random Processes, a bit of Linear Algebra. 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 :

The books are listed in the increasing order of difficulty in depth and presentation.

  1. Probability and Stochastic Processes - A friendly Introduction for Electrical and Computer Engineers - Roy D Yates, david J Goodman
  2. Probability and Stochastic Processes - Leon Garcia
  3. Linear Algebra and Its Applications - Gilbert Strang
  4. Probability and Stochastic Processes - A friendly Introduction for Electrical and Computer Engineers - Roy D Yates, david J Goodman
  5. Probability and Stochastic Processes - 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

To be updated 

Doctoral Students

  1. Mr Thiruppathirajan Sankaralingam, VSSC, Enhanced Sparsity Order Estimation Techniques for Dynamic Compressing 

Masters Students

  1. 2013-14 : Srujana Lily,
  2. 2015-16 : Raveen, 
  3. 2018-19 : Deepti Sivan : Signal Synchronization in Indian Regional Navigational Satellite
  4. 2018-19 : Chittella V S K Krishnan : Study of IRNSS Receiver Design 
  5. 2018-19 : Ankit Kumar Gupta  : Study of the Design of CCSDS Compliant Turbo Decoder 
  6. 2019-20 : Gokul P N : Sensor Fusion for Autonomous Driving
  7. 2022-23 : Mukul Kumar Jobra : Drone Detection and Tracking System Development

 

 

 

1. Robust Signal Processing

2. Dynamic Compressed Sensing

The details will uploaded shortly.

Dear Visitor, 
    I have given links to some very interesting popular science books that I relished as a student. Most of them were published by the famous Soviet publisher MIR. Today these aren't available in the market, however have been scanned and archived by some good samaritans for posterity. Even if you aren't scientifically inclined, you may benefit from reading some of these science books that I have listed below. The download links are also given below. Personally, I found these books to be more interesting  than many of the popular science books available in the market today.
 
Mathematics
1. Did you say mathematics is a wonderful book for any student. it covers quite a few branches of mathematics without a single equation. Basically, it's a good story book on mathematics.
 
https://archive.org/details/yakov-khurgin-did-you-say-mathematics-mir-publishers-1984
 
2. The world is built on probability. Another classic introduction to basics of probability published by MIR publisher and authored by Lev Tarasov. It related probability with many other branches of science and mathematics.
https://archive.org/details/TheWorldIsBuiltOnProbability
 
3. Yet another interesting book by Lev Tarasov on symmetry and its manifestations in the physical world. The second part of the book deals with symmetry in subatomic physics. The book is richly illustrated.
 
4. Funs with maths and physics - Authored by Yakovv Perelman
https://archive.org/details/FunWithPhysicsAndMaths-English-BrianTeasersTricksIllusions
 
Physics and Astronomy
 
 
 
4. An excellent advanced problem solving guide to physics - useful at school as well as university level is
https://archive.org/details/BelikovGeneralMethodsForSolvingPhysicsProblems
 
Chemistry
1.Experiments without explosion.
https://archive.org/details/ExperimentsWithoutExplosions
It contains experiments in chemistry.
 
 
 

Little Mathematics Library Booklets 

1. Remarkable Curves                                                     https://archive.org/details/lml-remarkable-curves
2. The Montecarlo Method                                               https://archive.org/details/TheMonte-carloMethodlittleMathematicsLibrary
3. The Shortest Lines - Variational Problems                   https://archive.org/details/lyusternik-the-shortest-lines-variational-problems-little-mathematics-library
4. Godels incompleteness Theorem                                https://archive.org/details/GodelsIncompletenessTheorem
5. Complex Numbers and Conformal mapping                https://archive.org/details/ComplexNumbersAndConformalMappingslittleMathematicsLibrary
6. Elements of Game Theory                                           https://archive.org/details/ElementsOfGameTheorylittleMathematicsLibrary
7. Inequalities                                                                   https://archive.org/details/InequalitieslittleMathematicsLibrary
8. Differentiation Explained                                              https://archive.org/details/boltyansky-v.-g.-differentiation-explained-little-mathematics-library-mir-1977
9. Lobachevskian Geometry https://archive.org/details/lobachevskiangeometry
10. Recursion Sequences https://archive.org/details/recursion-sequences
11. Induction in Geometry https://archive.org/details/little-mathematics-library-l.-i.-golovina-and-i.-m.-yaglom-induction-in-geometry
12. The Kinematic Method in Geometrical Problems https://archive.org/details/LyubichShorTheKinematicMethodInGeometricalProblemsLMLMir1980/page/n9/mode/2up
13.. Proof in Geometry https://archive.org/details/fetisov-proof-in-geometry-little-mathematics-library
14. Pascal's Traingle https://archive.org/details/uspensky-pascals-triangle-plm
15. The Fundamental Theorem of Arithmetic https://archive.org/details/TheFundamentalTheoremOfArithmetic
16. Method of Successive Approximations https://archive.org/details/vilenkin-method-of-successive-approximations-lml
17. Geomtrical Constructions With Compasses Only https://archive.org/details/kostovskii-geometrical-constructions-with-compasses-only-little-mathematics-library
18. Systems of Linear Inequalities https://archive.org/details/SystemsOfLinearInequalitieslittleMathematicsLibrary
19. Solving Equation in Integers https://archive.org/details/SolvingEquationsInIntegerslittleMathematicsLibrary
20. Algebraic Equations of Arbitrary Degree https://archive.org/details/AlgebraicEquationsOfArbitraryDegreelittleMathematicsLibrary
21. Systems of Linear Equations https://archive.org/details/skornyakov-systems-of-linear-equations-little-mathematics-library
22. Posts' Machine https://archive.org/details/uspensky-lml-posts-machine-mir-1983
23. An Unusual Algebra https://archive.org/details/an-unusual-algebra-little-mathematics-library
24. Fascinating Functions https://archive.org/details/FascinatingFractionslittleMathematicsLibrary
25. Method of Coordinates https://archive.org/details/MethodOfCoordinateslittleMathematicsLibrary
26. Areas and Logarithms https://archive.org/details/AreasAndLogarithmslittleMathematicsLibrary
27. Stereographic Projection https://archive.org/details/stereographic-projection-little-mathematics-library
28. Plotting Graphs https://archive.org/details/PlottingGraphslittleMathematicsLibrary
29. Dividing A line Segment in Given Ratio https://archive.org/details/DividingALineSegmentInGivenRatiolittleMathematicsLibrary
30. Systems of Linear Inequalities https://archive.org/details/systemsoflineari0000asso
31. Calculus of Rational Function https://archive.org/details/CalculusOfRationalFunctionslittleMathematicsLibrary
32. Proof in Geometry https://archive.org/details/fetisov-proof-in-geometry-little-mathematics-library
33. Images of Geometric Solids https://archive.org/details/BeskinNMImagesOfGeometricSolidsMir1985B0006EM1NY
 
 
 

Journals     

  1. Sheetal Kalyani, Raghavendran Lakshminarayanan, Krishnamurthy Giidhar : Biased Estimators with Adaptive Shrinkage Targets for Orthogonal Frequency Division Multiple Access Channel Estimation. IET Commun. 7(1):13-22 (2013)
  2. Sparsity Order Estimation for Compressed Sensing System Using Sparse Binary Sensing Matrix S., Thiruppathirajan; R., Lakshmi Narayanan; S., Sreelal; Manoj B. S. Article IEEE Access, Volume 10, Year 2022, Pages 33370-33392 DOI:10.1109/ACCESS.2022.3161523  
  3. Maximum Likelihood Estimation of Time-Varying Sparsity Level for Dynamic Sparse Signals, Thiruppathirajan S.;Lakshmi Narayanan R.; Sreelal S.;Manoj B.S.Article IEEE Access, Volume 9, Year 2021, Pages 136687-136701 DOI:10.1109/ACCESS.2021.3113871 
Conferences : 
  1. H-infinite Channel Estimation for Cellular OFDM, R Lakshminarayanan, K Giridhar 2007 IEEE Wireless Communications and Networking Conference, 1417-1421
  2. Mean square robustness of linear game theoretic estimators, R Lakshminarayanan, K Giridhar, 2010 National Conference On Communications (NCC), 1-5

Patents : 

1. Robust Channel Estimation of OFDM Systems. The details regarding tha patent can accessed at https://patents.google.com/patent/US20130215826