### Basic Information

- Course: Applied and Computational Harmonic Analysis
- Lecture: Tuesdays and Thursdays, 12:40pm – 2:00pm,
~~Wells Hall A118~~online via Slack/Zoom - Office hours: Monday – Thursday, 4:00pm – 5:00pm,
~~Engineering Building 2507F~~online via Slack/Zoom - Syllabus

### Announcements

- [Apr 23] A combined pdf with all lectures in one document is now available.
- [Apr 23] Lectures 27 and 28 are posted. They include
**Exercises 73-79**, which are**optional and do not need to be turned in**. - [Apr 18] There was a typo in Exercise 70, which has been corrected.
- [Apr 17] Lectures 25 and 26 are posted. They include
**Exercises 63-72**, which are due**Friday, April 24**. - [Apr 09] Lectures 23 and 24 are posted. They include
**Exercises 58-62**, which are due**Thursday, April 16**. - [Apr 02] Lectures 21 and 22 are posted. They include
**Exercises 54-57**, which are due**Thursday, April 9**. - [Mar 26] Lecture 20 is posted. There are no exercises. I will give some exercises once we finish our discussion of stochastic processes (probably after class on March 31). In the meantime, if you want to learn more, check out the references in the notes!
- [Mar 24] Lectures 18 and 19 are posted.
**[Mar 16] No lecture on Tuesday (March 17). Office hours are cancelled Monday – Wednesday (March 16-18). Office hours (online) will resume Thursday (March 19), and class (via Zoom) will resume also on Thursday (March 19).**- [Mar 12] Lecture 17 is posted.
**Exercise 53**is included (just reading). - [Mar 12] Small update to Lecture 16 – corrected a typo in Exercise 51(a).
**[Mar 11] Class will done remotely via Zoom. More details will be posted in Slack and sent via email.****[Mar 11] There is now a Slack for the class. The link to join has been sent by email. If you did not receive that email, please let me know. In particular, if you are not officially registered for the class, please email me ASAP so I can add your email to the list.**- [Mar 10] Lecture 16 is posted.
**Exercises 51-52**are included and are due**Thursday, March 19**. - [Feb 27] Lectures 14 and 15 (combined into one file) are posted. They include
**Exercises 48-50**, which are due**Thursday, March 12**. Also note, the proof of Theorem 5.5 has been cleaned up a bit more, even beyond what we did in class today (February 27). In particular note Proposition 5.6 (contained within the proof of Theorem 5.5) and the bounding of I_J and II_J. - [Feb 21] Lectures 12 and 13 are posted. Collectively they include
**Exercises 41-47**, which are due**Thursday, February 27**. - [Feb 13] Lecture 11 is posted.
**Exercises 39-40**are included and are due**Thursday, February 20**. - [Feb 13] Lecture 10 is posted.
**Exercises 37-38**(all reading) are included. - [Feb 09]
**Exercises 27-36**are now due**February 20**! Note: There may be one or two more exercises added in this week that will also be due February 20. - [Feb 09] Updated lecture 09 to add a clarifying note for
**Exercise 34(b)**. - [Feb 09] Updated lecture 08 to fix a typo in
**Exercise 30.** - [Feb 06] Lecture 09 is posted.
**Exercises 33-36**are included and are due**Thursday****,****February 13****February 20**. - [Feb 06] Updated lecture 08 to simplify
**Exercise 32(b)**! - [Feb 05] Lecture 08 is posted.
**Exercises 27-32**are included and are due**Thursday,**.~~February 13~~February 20 - [Jan 30] Lecture 07 is posted.
**Exercises 24-26**are included and are due**Thursday, February 6**. - [Jan 28] Lecture 06 is posted.
**Exercises 19-23**are included and are due**Thursday, February 6**. - [Jan 24] Lecture 05 is posted.
**Exercises 14-18**are included and are due**Thursday, January 30**. - [Jan 21] Lecture 04 is posted.
**Exercises 10-13**are included and are due**Thursday, January 30**. - [Jan 16] Lecture 03 is posted.
**Exercises 6-9**are included and are due**Thursday, January 23**. - [Jan 14] The classroom has been moved (for the final time, hopefully) to Wells Hall A118! The syllabus has been updated to reflect the new time and the new room.
- [Jan 14] Lecture 02 notes are posted!
**Exercises 4-5**are included and are due**Thursday, January 23**. - [Jan 13] Class time has been moved to 12:40pm – 2:00pm!
- [Jan 13] The lecture on January 14 will be in Wells Hall C204A!
- [Jan 13] Formatting of lecture 01 notes has been updated. Content is the same!
- [Jan 9] Lecture 01 notes + slides are posted.
**Exercises 1-3**(all reading) are in the lectures notes! - [Jan 9] The class room will be moved again, stay tuned!
- [Jan 9] The class room has been moved to Wells Hall C117 in order to try to give us a little more space.
- [Jan 3] Class will start Thursday, January 9. There is no lecture on January 7!

### Lecture Notes

All lectures in one document: here

- lecture 01 + day 01 slides
- lecture 02
- lecture 03
- lecture 04
- lecture 05
- lecture 06
- lecture 07
- lecture 08
- lecture 09
- lecture 10
- lecture 11
- lecture 12
- lecture 13
- lectures 14 & 15
- lecture 16
- lecture 17
- lectures 18 & 19
- lecture 20
- lectures 21 & 22
- lectures 23 & 24
- lectures 25 & 26
- lectures 27 & 28

### Resources

- A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edition, Stéphane Mallat (required textbook)
- Wavelets and Operators, Yves Meyer
- Foundations of Time Frequency Analysis, Karlheinz Gröchenig
- Harmonic Analysis and Applications, John Benedetto
- Stochastic Calculus for Finance II, Steven Shreve
- Introduction to Random Fields and Scale Invariance, Hermine Biermé
- Fractional Brownian motion in a nutshell, Georgiy Shevchenko