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Justin Romberg
Email: jrom@ece.gatech.edu
Office: Centergy 5227
Phone: 404-894-3930

ECE 6250 is a general purpose, advanced DSP course designed to follow an introductory DSP course. The central theme of the course is the application of tools from linear algebra to problems in signal processing.

Download a syllabus (pdf)


I. Signal representations in vector spaces
   Introduction to discretizing signals using a basis:
       the Shannon-Nyquist sampling theorem
       Fourier Series
 &nbsp     polynomials and splines
   linear vector spaces, linear independence, and basis expansions
   norms and inner products
   orthobases and the reproducing formula
   Parseval’s theorem and the general discretization principle
   signal approximation in an inner product space
   Gram-Schmidt and the QR decomposition

II. Linear inverse problems
   introduction to linear inverse problems, examples
   the singular value decomposition (SVD)
   least-squares solutions to inverse problems and the pseudo-inverse
   stable inversion and regularization
   weighted least-squares and linear estimation
   least-squares with linear constraints

III. Computing the solutions to large-scale least-squares problems
   Cholesky and LU decompositions
   structured matrices: Toeplitz, diagonal+low rank, banded
   large-scale systems: steepest descent
   large-scale systems: the method of conjugate gradients

IV. Low-rank updates for streaming solutions to least-squares problems
   recursive least-squares
   the Kalman filter

V. Matrix approximation using least-squares
   low-rank approximation of matrices using the SVD
   total least-squares
   principal components analysis

VI. Beyond least-squares (topics as time permits)
   gradient descent, Newton’s method for convex optimization
   constrained optimization
   L1 approximation and regularization
   independent components analysis