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Instructor
Justin Romberg
email-gatech
Office: Centergy 5245
Phone: 404-894-3930

Description
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)

Outline

I. Sampling and filter banks
   the Shannon-Nyquist sampling theorem
   multirate digital signal processing
   filter banks and the discrete wavelet transform

II. Signal representations in vector spaces
   linear vector spaces, linear independence, and basis expansions
   norms and inner products
   orthobases, the reproducing formula, and Parseval’s theorem
   signal approximation in an inner product space
   Gram-Schmidt and the QR decomposition

III. 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

IV. Computing the solutions to large-scale least-squares problems
   structured matrices
   steepest descent
   the conjugate gradient method

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

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

VII. Beyond least-squares (topics as time permits)
   norm approximation problems
   non-smooth regularization for linear inverse problems
   independent components analysis
   linear programming for L1 and Linfinity problems