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Coursebooks
Mathematical foundations of signal processing
COM-514
Lecturer(s) :
Kolundzija MihailoParhizkar 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)
No
Bibliography
M. Vetterli, J. Kovacevic and V. Goyal, "Signal Processing: Foundations", Cambridge U. Press, 2014.
Available in open access at http://www.fourierandwavelets.org
Ressources en bibliothèque
Websites
Moodle Link
In the programs
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
- SemesterFall
- Exam formWritten
- 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
- Semester
Reference week
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14-15 | INM203 | ||||
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legend
- Autumn semester
- Winter sessions
- Spring semester
- Summer sessions
- Lecture in French
- Lecture in English
- Lecture in German