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 Manolaki

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.

https://archive.org/details/ThisAmazinglySymmetricalWorld

4. Funs with maths and physics - Authored by Yakovv Perelman
https://archive.org/details/FunWithPhysicsAndMaths-English-BrianTeasersTricksIllusions

Physics and Astronomy

1.  Astronomy for entertainment
https://archive.org/download/AstronomyForEntertainment

2.  Physics fo entertainment
http://www.arvindguptatoys.com/arvindgupta/physicsforentertainment.pdf

3. Non-mathematical puzzles in physics.
https://archive.org/details/v.-n.-lange-physical-problems-for-robinsons-mir-publishers-1976

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.

2. https://archive.org/details/silhouettesofchemistry

Physics for Everyone Series - by The Nobel Laurate Landau with Kataigorodsky - Not for the mathematically oriented (No formulae in it.).
1. https://archive.org/details/PhysicsForEveryone-Book1-PhysicalBodies
2. https://archive.org/details/PhysicsForEveryone-Book2-Molecules
3. https://archive.org/details/PhysicsForEveryone-Book3-Electrons
4. https://archive.org/details/LandauKitaigorodskyPhysicsForEveryoneMotionHeatMir1978


Some Problem Books in Physics

1. An interesting physics problem book - not very difficult ones by shalnov and others https://archive.org/details/ZubovShalnovProblemsInPhysicsMir
2. https://archive.org/details/questions-and-answers-in-school-physics
3. Olympiad problems https://archive.org/details/ptitudetestproblemsinphysics

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