ECE 6250: Advanced Topics in Digital Signal Processing

Fall 2019

  • Overview
  • Course Notes
  • Assignments

Signal representations in vector spaces

  • The Shannon-Nyquist sampling theorem
  • A first look at basis expansions
  • Vector spaces, subspaces, and finite-dimensional bases
  • Norms and inner products [Filled]
  • Linear approximation in a Hilbert space
  • Orthogonal bases [Filled]
  • Othogonal projections and the Gram-Schmidt algorithm
  • Cosine transforms and image compression
  • The lapped orthogonal transform
  • Wavelets (I)
  • Wavelets (II)
  • Riesz bases
  • B-splines

Linear inverse problems and least-squares signal processing

  • Discretizing inverse problems
  • Solving symmetric systems of equations
  • The singular value decomposition
  • Stable least-squares
  • Total least-squares and principal component analysis

Computing the solution to least-squares problems

  • Solving systems of equations: Matrix factorizations and structured systems
  • Iterative methods for least-squares
  • Streaming least-squares problems
  • Kalman filtering and the LMS algorithm
  • Kernel methods

Supplemental notes

  • Review of Fourier transforms
  • Basic matrix manipulations