Schedule

Event

Date

Description

Course Material
Lecture

09/25/2025
Thursday

Course introduction and signal-processing review
[notes]
- Filters and LTI systems
- discrete-time Fourier transforms
- z-Transforms
- Linear-phase filters
Lecture

09/30/2025
Tuesday

Linear-phase and all-pass filters
[notes]
- Linear-phase filters and group delay
- All-pass filters
- Minimum-phase systems
- Maximum-phase systems
Lecture

10/02/2025
Thursday

Introduction to multirate systems and upsampling
[notes]
- Introduction to filter banks
- Upsampling
- Interpolation filters (low-pass and high-pass)
- Homework 1 Out
Lecture

10/07/2025
Tuesday

Upsampling and downsampling
[notes]
- General case of upsampling
- General case of downsampling
- Aliasing and antialiasing
- Multirate/Noble identities
- Homework 1 Solution
Lecture

10/09/2025
Thursday

Polyphase representations
[notes]
- Fast implementations of multirate filtering
- Even and odd polyphases
- z-domain and time-domain characterizations of polyphases
Exam

10/09/2025 09:30
Thursday

Quiz 1
Due

10/10/2025 23:55
Friday

Project Group Selection
Lecture

10/14/2025
Tuesday

Polyphase representations and two-channel filter banks
[notes]
- General case of M polyphases
- Two-channel filter banks
- Perfect-reconstruction conditions
- Homework 2 Out
Lecture

10/16/2025
Thursday

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
Lecture

10/21/2025
Tuesday

Polyphase representation of filter banks
[notes]
- Analysis and synthesis polyphase matrices
- PR conditions based on polyphase matrices
- Haar wavelet filters
- Homework 2 Solution
Lecture

10/23/2025
Thursday

Orthogonal filter banks
[notes]
- Haar wavelet filters
- Orthogonal filter banks and paraunitary polyphase matrices
- Filter constraints for orthogonal filter banks
Exam

10/23/2025 09:30
Thursday

Quiz 2
Lecture

10/28/2025
Tuesday

Popular wavelet filters
[notes]
- Haar wavelet filters
- Daubechies filters
- Biorthogonal wavelet filters
- Symlet filters
- Homework 3 Out
Lecture

10/30/2025
Thursday

DWTs and generalized sampling
[notes]
- Discrete wavelet transforms (DWTs)
- Sampling review
- Generalized and non-ideal sampling
Due

11/01/2025 23:55
Saturday

Project Proposal
Lecture

11/04/2025
Tuesday

Introduction to multiresolution
[notes]
- Generalized sampling
- Approximation and detail spaces
- Introduction to multiresolution analyses (MRAs)
- Homework 3 Solution
Lecture

11/06/2025
Thursday

Multiresolution analyses
[notes]
- Multiresolution analyses (MRAs)
- Wavelet bases
- Filters from scaling functions and wavelets
Exam

11/06/2025 09:30
Thursday

Quiz 3
Exam

11/25/2025 09:30
Tuesday

Midterm Exam
Due

12/11/2025 23:55
Thursday

Project Report + Presentation Slides