525.762.81 - Introduction to Wavelets

Electrical and Computer Engineering
Fall 2023

Description

This is an introductory course on wavelet analysis, with an emphasis on the fundamental mathematical principles and basic algorithms. We cover the mathematics of signal (function) spaces, orthonormal bases, frames, time-frequency localization, the windowed Fourier transform, the continuous wavelet transform, discrete wavelets, orthogonal and biorthogonal wavelets of compact support, wavelet regularity, and wavelet packets. It is designed as a broad introduction to wavelets for engineers, mathematicians, and physicists.Prerequisite: Competence with multivariable calculus, linear algebra, and a scientific programming language is required, as well as familiarity with Fourier transforms and signal processing fundamentals such as the discrete Fourier transform, convolutions, and correlations.

Expanded Course Description

A good link to read about the subject:

https://www.quantamagazine.org/how-wavelets-allow-researchers-to-transform-and-understand-data-20211013/

Instructor

Profile photo of Amir-Homayoon Najmi.

Amir-Homayoon Najmi

ahnajmi@jhu.edu

Course Structure

The course materials are divided into 14 modules which can be accessed by clicking Course Modules. Each module is divided into one or more videos, and includes a homework assignment.

Course modules will become available on Saturdays with assignments due on Tuesdays (10 days later) at midnight.

Course Topics


Course Goals

Thorough understanding of the mathematical structures of signal and function spaces underlying theory of wavelets and multi-resolution analysis, and implementing wavelet transform algorithms for analysis and compression of time series and images.

Course Learning Outcomes (CLOs)

Textbooks

Amir-Homayoon Najmi:  “Wavelets:  A Concise Guide”, Johns Hopkins University Press, 2012. 
ISBN:  978-1-4214-0496-7 (paperback – also available as Ebook),

Required Software

Matlab, IDL, Python, or equivalent. 

Student Coursework Requirements

It is expected that each module will take approximately 7–13 hours per week to complete. The lectures will take between 1.5-3 hours. I expect you to read the relevant chapters and sections of the required text for about 1-2 hours. The homework assignments should take 3-8 hours.

This course will consist of three basic student requirements:

  1. Preparation and Participation (Module Discussions) (15% of Final Grade Calculation)

    Each week you are required to complete a discussion post explaining points or concepts that challenged you most. These will help me to offer guidance and feedback, as well as providing the opportunity for other students to offer their experience and thoughts. Discussions take place using the Discussion thread (please do not create new threads and do not post discussions in the Q & A thread). Try to be as detailed as possible in your postings and in your responses to your classmates' postings. Please ensure that your postings are civil and constructive. You may mention and discuss any scientifically reputable link(s) pertaining to the discussion.

    Student Question and Answer (Q & A) – will be available each week so that students can interact with each other and ask questions on the homework/resources of the week. These should take place using the Q & A thread. I will monitor them and post anything that I feel everyone in class would benefit from.
  2. Computational problems / Computer implementations (85% of Final Grade Calculation)

    Computational problems and computer implementations will be relevant to the learning objectives and will be assigned a letter grade (A+,A, A-,B+,B,B-,…) for each assignment. Each assignment’s letter grade is a reflection of what a final grade might be if this single assignment were to be used to determine a final grade. The final grade will be based on 14 equally weighted homework problem sets. Each homework set is approximately 6% of the 85% of the total grade, i.e., 6 x 14 sets is approximately 85% of the total grade.

    Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the computations/calculations, and conclusions/discussion delineated. All figures and tables should be captioned and labeled appropriately. You should include your computer code, as a separate file in its native format, for possible help with “debugging”. The assignment itself must be in PDF format and very legible (scanned page images are unacceptable); I highly recommend using a typesetting program (e.g., LaTex) to produce your PDF output.|

    All assignments are due according to the dates in the Module checklist, homework set instructions and/or Calendar. Multiple attempts will be granted in cases that are deserved; should you be asked to make a second attempt then you must submit your second attempt within 1 week so as to receive full credit.

    Please make prior arrangements if you think your submission will be late; otherwise the maximum achievable grade may be lowered on a late homework. Homework grades will be sent within 7- 10 days after submission.



Final grades will be determined by the following weighting:

Item

% of Grade

Module Discussions (“Muddiest Points”)

15%

Weekly assignments

85%


Grading Policy

Assignments are due according to the dates discussed above (Course Structure). Grades will be posted 7-9 days after homework due date.

A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week.

A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

Grading Schema:

Score RangeLetter Grade
100-98= A+
97-94= A
93-90= A−
89-87= B+
86-83= B
82-80= B−
79-70= C
<70= F

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.