Apma 990 - Introduction to Wavelets

Outline

Fourier Transform

A brief overview and review of the Fourier transform.
  1. Continuous transform
  2. Discrete transform
  3. Windowed transform
  4. Applications

Introduction to Wavelets

  1. Lowpass/Highpass Filter
  2. Filter Bank
  3. Scaling function and Wavelets
  4. Wavelet transforms by mutliresolution

Filters

  1. Ideal filters, Shannon sampling, Sinc wavelets
  2. Filter design
  3. Fourier analysis
  4. Bases and Frames

Filter Banks

  1. Perfect reconstruction
  2. Polyphase matrix
  3. Efficient filter banks
  4. Polyphase for upsampling and reconstruction
  5. Lattice structure

Wavelet Transform

  1. Continuous transform
  2. Discrete transform
  3. Cascade algorithm

Orthonormal Bases

  1. Orthogonal filter banks
  2. Halfband filters, spectral factorization
  3. Maxflat (Daubechies) filters
  4. Multiresolution Analysis
  5. Compactly supported wavelets

Signal Processing Applications

  1. Image and Video compression
  2. Speech and audio compression