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Topic 1: Background Material

  • Adaptive filtering: Concepts and applications
  • Discrete-time signal processing
  • Stationary processes and models
  • Spectrum analysis
  • Linear algebra: Eigenanalysis and matrix decompositions

    Topic 2: Wiener Filtering

  • Minimum mean square error (MMSE) and the orthogonality principle
  • Digital Wiener filter and Wiener-Hopf equations
  • Constrained linear MMSE estimation
  • Applications: Minimum variance beamforming

    Topic 3: Linear Prediction

  • Forward and backward prediction
  • Levinson-Durbin algorithm
  • Lattice filters
  • Applications: DPCM speech coding

    Topic 4: Stochastic Methods

  • Steepest Descent algorithm
  • Least-Mean-Square (LMS) algorithm
  • Properties of the LMS
  • Normalized and frequency-domain LMS
  • Gradient adaptive lattice methods
  • Recursive LMS (RLMS) for adaptive IIR filtering
  • Applications: Active noise control and echo-cancellation

    Topic 5: Least Squares Methods

  • Least squares and orthogonality
  • Recursive least squares adaptive algorithms
  • Properties of RLS
  • Applications: ADPCM speech encoding

    Topic 6: Non-Linear Methods

  • Bussgang algorithms for blind deconvolution
  • Adaptive filters based on higher-order statistics
  • Applications: Blind channel equalization