ECE 251C - Filter Banks and Wavelets - Parhi [FA24]

Course Location: Jacobs Hall (EBU1), Room 2315
Course Time: Tuesday/Thursday 09:30 – 10:50

 

Instructor: Rahul Parhi
Email: rahul@ucsd.edu
Office Hours: Friday 16:00 – 17:30
Office: Jacobs Hall, Room 6406

 

TA: Prabhav Gaur
Email: pgaur@ucsd.edu
Office Hours: Thursday 14:00-15:00, Jacobs Hall Room 4506
                        Friday 11:00-12:00, Zoom: https://ucsd.zoom.us/j/97267357377

 

Main Reference:

Wavelets and Filter Banks by Gilbert Strang and Truong Nguyen, 1997, Wellesley-Cambridge Press.

The tentative plan is to cover Chapters 1–7.

 

Other References:

A Wavelet Tour of Signal Processing: The Sparse Way by Stephane Mallat, 1998, Elsevier Science.

Wavelets and Subband Coding by Martin Vetterli and Jelena Kovacevic, Prentice Hall, 1995.


Prerequisite: Basic knowledge of DSP (e.g., ECE 161A)


Grading:

  • In-class midterm exam (closed book, one page of handwritten notes) on November 14, 2024 (30%)
  • Project (70%)
    • Group Selection (2–3 students per group) due October 4, 2024 at 11:55pm
    • Project Proposal due October 31, 2024 at 11:55pm
    • Project Presentation (In-class on December 3, 2024 and December 5, 2024 from 9:00 - 10:50 (35%)
    • Project Report due December 12, 2024 at 11:55pm (35%)
  • Homework (and solutions) will be handed out periodically (0%)


Note: I am traveling on October 22 and October 24. There will be prerecorded lectures posted on Canvas.

 

Questions: All questions about the course (logistical or technical) should be posted on Piazza.

 

The purpose of the lectures is to cover theory of filter banks and wavelets. The purpose of the project is to explore applications of filter banks and wavelets.

 

Topics Covered:

  • Week 0: Sep. 26
    • introduction and review of basic DSP
    • linear-phase systems
  • Week 1: Oct. 1 and Oct. 3
    • linear-phase systems
    • all-pass systems
    • introduction to multirate systems
  • Week 2: Oct. 8 and Oct. 10
    • multirate operations
      • upsampling
      • downsampling
    • noble identities
    • polyphase representations
  • Week 3: Oct. 15 and Oct. 17
    • polyphase representation
    • two-channel filter banks
      • perfect reconstruction conditions
      • general design procedure
  • Week 4: Oct. 22 and Oct. 24
    • general design procedure for two-channel filter banks
      • popular examples of factorizations of the product filters
      • popular examples of wavelet filters
    • polyphase representation of two-channel filter banks
    • orthogonal two-channel filter banks
  • Week 5: Oct. 29 and Oct. 31 🎃
    • orthogonal two-channel filter banks
    • discrete wavelet transform (DWT)
    • introduction to multiresolution
  • Week 6: Nov. 5 and Nov. 7
    • multiresolution analysis (MRA)
    • Haar wavelet basis of L2(R)
    • filters from wavelets
  • Week 7: Nov. 12 and Nov. 14
    • wavelets from filters
    • fundamental theorem of wavelet analysis
    • MIDTERM ON THURSDAY
  • Week 8: Nov. 19 and Nov. 21
    • time-frequency tilings of different signal representations
    • vanishing moments
    • decay of Fourier vs. wavelet coefficients
  • Week 9: Nov. 26
    • Fourier vs. wavelet approximation
    • denoising by soft-thresholding
    • THANKSGIVING ON THURSDAY 🦃
  • Week 10: Dec. 3 and Dec. 5
    • in-class project presentations
      • CLASS WILL BE FROM 9:00 - 10:50 THIS WEEK