525.780.8VL - Multidimensional Digital Signal Processing

Electrical and Computer Engineering
Spring 2023

Description

The fundamental concepts of multidimensional digital signal processing theory as well as several associated application areas are covered in this course. The course begins with an investigation of continuous-space signals and sampling theory in two or more dimensions. The multidimensional discrete Fourier transform is defined, and methods for its efficient calculation are discussed. The design and implementation of two-dimensional non-recursive linear filters are treated. The final part of the course examines the processing of signals carried by propagating waves. This section contains descriptions of computed tomography and related techniques and array signal processing. Several application oriented software projects are required.

Instructor

Profile photo of Brian Jennison.

Brian Jennison

bjennis1@jhu.edu

Course Structure

This course uses the Virtual Live (VL) format. All students participate online through live web-conferencing at the scheduled day and time. This is a synchronous online course in which students participate in live weekly lectures and discussions, and are able to interact with the instructor. All classes are recorded for download and review. Note that VL courses are not designed for asynchronous learning in the same way that online courses are. Rather, VL is essentially a face-to-face course but delivered via web-conferencing software. While the course lectures will be recorded, it is my expectation that students participate in the course synchronously if possible. I recognize that most of you are working professionals and conflicts will arise on occasion. So, please engage with me to seek accommodations that work for both of us.

Course Topics

  1. Review of One-Dimensional Digital Signal Processing
1. Continuous-Time Signals
1.1. Continuous-Time Fourier Series (CTFS)
1.2. Continuous-Time Fourier Transform (CTFT)
2. Discrete-Time Signals
2.1. Discrete-Time Fourier Series (DTFS)
2.2. Discrete-Time Fourier Transform (DTFT)
2.3. Linear-Time Invariant (LTI) Systems
3. Sampling Theorem
4. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)
5. Finite Impulse Response (FIR) Filter Design (Windowing and Equiripple methods)
6. Multi-rate Signal Processing and Interpolation

 

  1. Multidimensional Digital Signal Processing Fundamentals
1. Two-dimensional Continuous-Space Fourier transform (CSFT)
2. Polar Coordinates and the Hankel transform
3. Rectangular sampling, hexagonal sampling, and arbitrary sampling lattices
4. Discrete-space signals
5. Periodicity in multidimensions
6. 2-D Discrete-Space Fourier Series, 2-D Discrete-Space Fourier Transform
7. Linear-Shift Invariant (LSI) systems
7.1. stability
7.2. convolution
8. 2-D Discrete Fourier Transform (DFT) and properties
9. 2-D Fast Fourier Transform (FFT) and row-column decompositions

 

  1. Two-dimensional FIR filter design
1. Zero-phase symmetry
2. 2-D Windowing
2.1.separable windows
2.2.circularly rotated windows
3. Designs via Frequency Transformations
4. Implementation of 2-D FIR filters

 

  1. Computed Tomography
1. Radon Transforms (continuous and discrete)
2. Projection-Slice Theorem
3. Direct Fourier-Domain Reconstruction
4. Convolution-backprojection
5. Connection to Synthetic Aperture Radar

 

  1. Array Signal Processing
1. Space-time signals and plane waves
2. Delay-and-sum beamforming
3. Beampatterns, array shading
4. Time-domain discrete-time interpolation beamforming
5. Frequency-domain beamforming
6. Optimum beamforming
7. Angle of Arrival Estimation

Course Goals

To acquire and demonstrate the skills needed to analyze multidimensional discrete-space signals and systems. Utilize these skills to solve practical problems in computed imaging and array signal processing.

Course Learning Outcomes (CLOs)

Textbooks

OPTIONAL

There is no formal textbook requirement for this course.  Course notes will be available on the Canvas site.

The following texts are references on multidimensional signal processing and may be useful for this course as additional resources:

Additionally, students are encouraged to consult any books on general (one-dimensional) digital signal processing they may already possess from previous classes.  An example is:

Required Software

MATLAB will be used extensively throughout the course. Students are welcome to use an alternate software application (e.g., Python) but instructor assistance will be limited.

Student Coursework Requirements

This course will consist of four basic components:

1. Weekly Synchronous Lectures

Weekly attendance is expected.  Please let the instructor know in advance if you will not be able to attend a lecture.

2. Homework (25% of Final Grade Calculation)

You will be given weekly homework assignments in the first half of the course.  MATLAB (or alternative) will be utilized to complete most of these assignments.  Your work will be due at the beginning of class on the due date, graded, and returned to you.  No late work will be accepted without prior arrangement with me. 

3. In-Class Examination (25% of Final Grade Calculation)

There will be one in-class examination near mid-semester.  Students will have the entire class period to work on the exam.  In working the exam, students may use the lecture notes, supplementary references and handouts, and a handheld calculator.

4. Two Course Projects (25% and 20% of Final Grade Calculation)

Two application-oriented projects will be assigned in the second half of the semester.  MATLAB (or alternative) will be required to complete these projects.  The second project will be assigned after the first is due, and both projects will be due two weeks after their date of assignment.

Grading Policy

Final grades will be determined by the following weighting:

Item

% of Grade

Homework

25%

Project 1

25%

Project 2

20%

Midterm Exam

25%

In-Class Participation

5%

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.