Coursebooks

Mathematical foundations of signal processing

COM-514

Lecturer(s) :

Kolundzija Mihailo
Parhizkar Reza
Scholefield Adam James

Language:

English

Summary

Signal processing tools are presented from an intuitive geometric point of view which is at the heart of all modern signal processing techniques. Student will develop the mathematical depth and rigor needed for the study of advanced topics in signal processing.

Content

From Euclid to Hilbert applied to inverse problems (vector spaces; Hilbert spaces; approximations, projections and decompositions; bases)

Sequences, Discrete-Time Systems, Functions and Continuous-Time Systems (flipped class review of discrete-time Fourier transform; z-transform; DFT; Fourier transform and Fourier series).

Sampling and Interpolation (sampling and interpolation with finite-dimensional vectors, sequences and functions)

Approximation and compression (polynomial and spline approximation, transform coding and compression)

Localization and uncertainty (time and frequency localization for sequences and functions, tiling the time-frequency plane)

Computerized tomography fundamentals (line integrals and projections, Radon transform, Fourier projection/slice theorem, filtered backprojection algorithm, algebraic reconstruction techniques).

Array signal processing fundamentals (spatial filtering and beamforming, adaptive beamforming, acoustic and EM source localization techniques).

Compressed sensing and finite rate of innovation (overview and definitions, reconstruction methods and applications)

Euclidean Distance Matrices (definition, properties and applications).

Learning Prerequisites

Required courses

Circuits and Systems

Signal processing for communications (or Digital signal processing on Coursera)

Learning Outcomes

By the end of the course, the student must be able to:

Master the right tools to tackle advanced signal and data processing problems
Develop an intuitive understanding of signal processing through a geometrical approach
Get to know the applications that are of interest today
Learn about topics that are at the forefront of signal processing research

Teaching methods

Ex cathedra with exercises

One week of flipped class

Expected student activities

Attending lectures, completing exercises

Assessment methods

Homeworks 20%, midterm (written) 30%, final exam (written) 50%

Supervision

Office hours	Yes
Assistants	Yes
Forum	No

Resources

Virtual desktop infrastructure (VDI)

Bibliography

M. Vetterli, J. Kovacevic and V. Goyal, "Signal Processing: Foundations", Cambridge U. Press, 2014.

Available in open access at http://www.fourierandwavelets.org

In the programs

Communication Systems - master program, 2019-2020, Master semester 1
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Communication Systems - master program, 2019-2020, Master semester 3
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computational science and Engineering, 2019-2020, Master semester 1
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computational science and Engineering, 2019-2020, Master semester 3
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computer Science - Cybersecurity, 2019-2020, Master semester 1
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computer Science - Cybersecurity, 2019-2020, Master semester 3
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computer Science, 2019-2020, Master semester 1
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computer Science, 2019-2020, Master semester 3
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Data Science, 2019-2020, Master semester 1
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Data Science, 2019-2020, Master semester 3
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Communication systems minor, 2019-2020, Autumn semester
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Computer and Communication Sciences (edoc), 2019-2020
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks
Systems Engineering minor, 2019-2020, Autumn semester
- Semester
  Fall
- Exam form
  Written
- Credits
  6
- Subject examined
  Mathematical foundations of signal processing
- Lecture
  3 Hour(s) per week x 14 weeks
- Exercises
  2 Hour(s) per week x 14 weeks

Reference week

	Mo	Fr
8-9
9-10
10-11
11-12
12-13
13-14
14-15	INM203
15-16	INM203	INM203
16-17	INM203	INM203
17-18
18-19
19-20
20-21
21-22

Lecture

Exercise, TP

Project, other

legend

Autumn semester
Winter sessions
Spring semester
Summer sessions

Lecture in French
Lecture in English
Lecture in German