You can download all of the lecture notes here. Please email me if you find any mistakes.

  • Course introduction and signal-processing review
    [notes]
    • Filters and LTI systems
    • discrete-time Fourier transforms
    • z-Transforms
    • Linear-phase filters
  • Linear-phase and all-pass filters
    [notes]
    • Linear-phase filters and group delay
    • All-pass filters
    • Minimum-phase systems
    • Maximum-phase systems
  • Introduction to multirate systems and upsampling
    [notes]
    • Introduction to filter banks
    • Upsampling
    • Interpolation filters (low-pass and high-pass)
    • Homework 1 Out
  • Upsampling and downsampling
    [notes]
    • General case of upsampling
    • General case of downsampling
    • Aliasing and antialiasing
    • Multirate/Noble identities
    • Homework 1 Solution
  • Polyphase representations
    [notes]
    • Fast implementations of multirate filtering
    • Even and odd polyphases
    • z-domain and time-domain characterizations of polyphases
  • Polyphase representations and two-channel filter banks
    [notes]
    • General case of M polyphases
    • Two-channel filter banks
    • Perfect-reconstruction conditions
    • Homework 2 Out
  • Design procedure of filter banks
    [notes]
    • General design procedure of two-channel FIR PR filter banks
    • Reduction to the design of Product filters
    • Type-I and Type-II design choices for product filters
  • Polyphase representation of filter banks
    [notes]
    • Analysis and synthesis polyphase matrices
    • PR conditions based on polyphase matrices
    • Haar wavelet filters
    • Homework 2 Solution
  • Orthogonal filter banks
    [notes]
    • Haar wavelet filters
    • Orthogonal filter banks and paraunitary polyphase matrices
    • Filter constraints for orthogonal filter banks
  • Popular wavelet filters
    [notes]
    • Haar wavelet filters
    • Daubechies filters
    • Biorthogonal wavelet filters
    • Symlet filters
    • Homework 3 Out
  • DWTs and generalized sampling
    [notes]
    • Discrete wavelet transforms (DWTs)
    • Sampling review
    • Generalized and non-ideal sampling
  • Introduction to multiresolution
    [notes]
    • Generalized sampling
    • Approximation and detail spaces
    • Introduction to multiresolution analyses (MRAs)
    • Homework 3 Solution
  • Multiresolution analyses
    [notes]
    • Multiresolution analyses (MRAs)
    • Wavelet bases
    • Filters from scaling functions and wavelets
  • Filters from wavelets
    [notes]
    • Filters from wavelets
    • MRA coefficients and DWTs
    • General wavelet analysis pipeline