Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Indian Institute of Science Bangalore

Mathematical Methods and Techniques in Signal Processing

Indian Institute of Science Bangalore and NPTEL via Swayam

This course may be unavailable.


  • 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.PRE-REQUISITES : UG in Digital Signal Processing, familiarity with probability and linear algebraINDUSTRY SUPPORT : Any company using DSP techniques in their work, such as, TI, Analog Devices, Broadcom and many more.Rajeev Motwani and Prabhakar Raghavan,Randomized Algorithms



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.

Taught by

Shayan Garani Srinivasa



Start your review of Mathematical Methods and Techniques in Signal Processing

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.