ACM 126a
Wavelets and Modern Signal Processing

Emmanuel Candes
300 Firestone

Office Hours: MF 11-12

Monday, Wednesday, Friday
2-2:55 p.m.
Keck 142






First lecture is on Wednesday, January 5.

Description: The aim of this two-term course is to cover the interactions existing between applied mathematics, namely applied and computational harmonic analysis, approximation theory, etc. and statistics and signal processing. Matlab will be the scientific programming language for this course. Assignments would typically involve a fair amount of scientific programming in matlab together with more classical exercises

Prerequisite: -
ACM 104 (Linear algebra), ACM 105 (Real analysis) or undergraduate equivalent or consent of instructor. Some programming experience or some willingless to learn. Prior knowledge of matlab not required.


  • The Fourier transform; the continuous Fourier transform, the discrete Fourier transform, FFT
  • Time-frequency analysis, short-time Fourier transform, Wigner Ville distribution
  • The wavelet transform; the continuous wavelet transform discrete wavelet transforms and orthogonal bases of wavelets
  • Wavelets and algorithms; fast wavelet transforms, wavelet packets, cosine packets.
These transforms have natural applications in the information sciences . The course will develop topics in:
  • Statistical estimation and applications to signal/image denoising
  • Inverse problems and applications to signal/image reconstruction
  • Linear and nonlinear approximation and applications to data compression


  1. Stephane Mallat"A Wavelet Tour of Signal Processing" Second edition, Academic Press (required)
  2. Stephane Jaffard, Yves Meyer and Robert Ryan"Wavelets: Tools for Science and Technology" SIAM, Philadelphia (optional)
  3. Yves Meyer"Wavelets and Operators"Cambridge University Press (optional)
  4. Ingrid Daubechies" Ten Lectures on Wavelets"SIAM, Philadelphia (optional)

I will do my best to post online all the handouts given in class. By the way, Sheila Shull (217 Firestone) is a person you can contact at any time (between 9:30am and 5pm) if you need administrative information. Her phone number is 626-395-4560.

Teaching Assistant and Office Hours:

Laurent Demanet, T 4-6, 210 Firestone


Homework assignments: 60%
  • Homework will generally be distributed on Wednesdays and due in class the following Wednesday.
  • There will be about 5 assignments, and your lowest score will be dropped in the final grade.
  • Late homeworks will NOT be accepted for grading (medical emergencies excepted with proof).

    Final exam: 40%. There will be a take-home final exam.