Mathematics of Signals and Systems

The files in this repository are developed for ECEn 671 taught in the Electrical and Computer Engineering Department at Brigham Young University. The purpose of the repository is to aid graduate students in learning common vector space and linear algebra techniques used in signal processing and control. The repository consists of two directories: The first containing lecture notes, written in beamer, and the second containing jupyter ipython notebooks written and edited by former students in my class. These contain working code examples and homework problems.

The textbook for the class is Moon & Stirling

Lecture Notes

ecen671_chap2.tex - metric, vector, normed, and inner product spaces, topology, orthogonality, linear operators, projections, Gram Schmidt Orthogonalization
ecen671_chap3.tex - approximation theory, dual approximation, underdetermined problems, generalized Fourier series
ecen671_chap4.tex - linear operators, matrix norms, adjoint operator, fundamental subspaces, matrix inverses, matrix condition number, Schur complement, recursive least squares.
ecen671_chap5.tex - LU Factorization, Cholesky Factorization, QR Factorization
ecen671_chap6.tex - Eigenvalues and eigenvectors, Jordan form, Cayley-Hamilton theorem, self adjoint matrices, invariant subspaces, quadratic forms, eigenfilters
ecen671_chap7.tex - singular value decomposition, pseudo inverse rank reducing approximations
ecen671_chap14.tex - gradient descent, LMS adaptive filtering, Gauss-Newton, Levenberg-Marquardt
ecen671_chap18.tex - constrained optimization, Lagrange multipliers, Kuhn-Tucker conditions

Student Designed Jupiter Notebooks

The following links have been developed by BYU graduate students enrolled in ECEn 671 Mathematics of Signals and Systems during Fall Semester 2018, and revised during Fall 2020.