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Courses » Mathematical Methods and Techniques in Signal Processing

Mathematical Methods and Techniques in Signal Processing

ABOUT THE COURSE:
  • Review of basic signals, systems and signal space: Review of 1-D signals and systems, review of random signals, multi-dimensional signals, review of vector spaces, inner product spaces, orthogonal projections and related concepts.
  • Sampling theorems (a peek into Shannon and compressive sampling), Basics of multi-rate signal processing: sampling, decimation and interpolation, sampling rate conversion (integer and rational sampling rates), oversampled processing (A/D and D/A conversion), and introduction to filter banks.
  • Signal representation: Transform theory and methods (FT and variations, KLT), other transform methods including convergence issues.
  • Wavelets: Characterization of wavelets, wavelet transform, multi-resolution analysis.

INTENDED AUDIENCE:
Post graduates and senior UGs with a strong background in basic DSP.

CORE/ELECTIVE: Core/elective

UG/PG: PG

PREREQUISITES:UG in Digital Signal Processing, familiarity with probability and linear algebra

INDUSTRY SUPPORT:Any company using DSP techniques in their work, such as, TI, Analog Devices, Broadcom and many more.

ABOUT THE INSTRUCTOR:



Dr. Shayan Garani Srinivasa received his Ph.D. in Electrical and Computer Engineering from Georgia Institute of Technology – Atlanta, M.S. from the University of Florida – Gainesville and B.E. from Mysore University. Dr. Srinivasa has held senior engineering positions within Broadcom Corporation, ST Microelectronics and Western Digital. Prior to joining IISc, Dr. Srinivasa was leading various research activities, managing and directing research and external university research programs within Western Digital. He was the chairman for signal processing for the IDEMA-ASTC and a co-chair for the overall technological committee. He is the author of a book, several journal and conference publications, holds U.S patents in the area of data storage. Dr. Srinivasa is a senior member of the IEEE, OSA and the chairman for the Photonic Detection group within the Optical Society of America. His research interests include broad areas of applied mathematics, physical modeling, coding, signal processing and VLSI systems architecture for novel magnetic/optical recording channels, quantum information processing, neural nets and math modeling of complex systems.

COURSE LAYOUT:

Week 1  : Review of vector  spaces, inner product spaces, orthogonal projections, state variable representation
Week 2  : Review of probability and random processes
Week 3  : Signal geometry and applications
Week 4  : Sampling theorems multirate signal processing  decimation and expansion (time and frequency domain effects)
Week 5  : Sampling rate conversion and efficient architectures, design of high decimation and interpolation filters, Multistage designs.
Week 6  : Introduction to 2 channel QMF filter bank, M-channel filter banks, overcoming aliasing, amplitude and phase distortions. 
Week 7  : Subband  coding and Filter Designs: Applications to Signal Compression
Week 8  : Introduction to multiresolution analysis and wavelets, wavelet properties
Week 9  : Wavelet decomposition and reconstruction, applications to denoising
Week 10  : Derivation of the KL Transform, properties and applications.
Week 11  : Topics on matrix calculus and constrained optimization relevant to KL Transform derivations.
Week 12  : Fourier expansion, properties, various notions of convergence and applications.

SUGGESTED READING MATERIALS:

  • Moon & Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice Hall, 2000. (required)
  • P. P. Vaidyanathan, Multirate systems and filter banks, Prentice Hall, 2000. (required)
  • A. Boggess & F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall, 2001.
  • G. Strang, Introduction to Linear Algebra, 2016.
  • H. Stark & J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 2014.
  • Class notes
CERTIFICATION EXAM :
  • The exam is optional for a fee.
  • Date and Time of Exams: April 28 (Saturday) and April 29 (Sunday) : Morning session 9am to 12 noon; 
  • Exam for this course will be available in one session on both 28 and 29 April.
  • Registration url: Announcements will be made when the registration form is open for registrations.
  • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.

CERTIFICATION:

  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 8 out of 12 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IISc. It will be e-verifiable at nptel.ac.in/noc.