Schedule

Topics:

• LTI systems
• DTFTs
• z-transforms
• linear-phase systems

Topics:

• linear-phase systems
• all-pass systems

Topics:

• all-pass systems
• minimum-phase systems
• maximum-phase systems
• multirate system example

Topics:

• upsampling and interpolation
• antialiasing and downsampling

Topics:

• antialiasing and downsampling
• Noble identities
• polyphase representations

Topics:

• polyphase representations
• two-channel filter banks
• perfect-reconstruction conditions

Topics:

• perfect-reconstruction conditions
• general design procedure

Topics:

• general design procedure
• factorizations of the product filter
• popular examples of wavelet filters
• polyphase representations of filter banks

Topics:

• polyphase representations of filter banks
• orthogonal filter banks

Topics:

• orthogonal filter banks

Topics:

• discrete wavelet transforms
• generalized sampling

Topics:

• generalized sampling
• multiresolution analysis
• Haar wavelet basis

Topics:

• multiresolution analysis
• filters from wavelets
• general wavelet analysis pipeline

Topics:

• general wavelet analysis pipeline
• wavelets from filters
• fundamental theorem of wavelet analysis

Topics:

• fundamental theorem of wavelet analysis
• wavelets and perfect-reconstruction filter banks
• time-frequency tilings
• vanishing moments

Topics:

• time-frequency tilings and the uncertainty principle
• decay of Fourier vs. wavelet coefficients

Topics:

• Fourier vs. wavelet approximation
• denoising by soft-thresholding