The Hidden Links in Communication Mathematics and Their Applications

Announcements

★★★ 2026/03/20 ★★★ Your Pi Day artwork has been uploaded to this webpage. Please scroll to the bottom of the page to find your creation :)

★★★ 2026/03/10 ★★★ Resources for the first programming assignment has been announced (see eCourse2 for the resources, and the assignment has been told in class); please submit your work before due date and late submission is not allowed! 

★★★ 2026/02/28 ★★★ This course will be delivered as an EMI (English-medium instruction) course, in line with the government’s bilingual education policy. This course is designed to show how linear algebra, differential equations, signals and systems, and probability are used in communication-system design. A solid background in these subjects is essential to keep up. Please do not take this course just for GPA boosting or as a basic review of prerequisites. Since this is the first time I’m offering the course, there will likely be room for improvement. Please leave feedback on eCourse2 as often as you can as it will directly help me refine the course.

Course Information

Instructor: Jian-Jia Weng

Time: Tuesdays and Thursdays, 08:45-10:00

Location: R103, Innovation Building

Office Hour: Upon Request

Teaching Method: Chalkboard Teaching with Video Recording Supplementary

Textbook: No Textbook for this course, but your textbooks on  linear algebra, differential equations, signals and systems, and probability will be helpful!!! 

 Grade Evaluation:  Homeworks (50%) + Final Project (25%) + Notes&In-Class Participation (25%) 

Contact Information

Office: R428, Innovation Building  (please make an appointment before coming)

Campus Internal Phone Number：33528

Email: jjweng AT ccu.edu.tw

If you have any questions regarding the course, you can email me from your school email account with:  

• Subject: [HLCM 2026] Inquiry - Your name and Student ID number (example: [HLCM 2026] Inquiry - 周杰倫 1234567)

• Contents: (1) topics you want to discuss and (2) your preferred time to meet in person (please specify at least 3 time slots)

for a special accommodation. I should reply to your email within 24hours; if not, please send the email again.

Tentative Schedule (To be updated)

• Week 1 (02/24, 02/26): 

  1. Overview of this course

  2. A Block Diagram of Communication Systems with Required Math

  3. Signals and Compression (e.g., Shannon-Niquist Sampling Theorem, review Signals and Systems, A. Oppenheim Sec. 7)

• Week 2 (03/03, 03/05): 

  1. Signal Modeling for Lossy Compression of Sampled Sequence

  2. Auto-Regressive Model with Least Square Optimization

  3. Linear Model with Probabilistic Method

• Week 3 (03/10, 03/12): No classes & A video recoding has been released on eCourse2

• Week 4 (03/17, 03/19):

  1. Data Representation using Different Bases

  2. Data-Independent Bases (Hadamard, Discrete Sine, and Discrete Cosine Bases)

  3. Data-Dependent Bases (Principal Component Analysis/Karhunen-Loeve Expansion)

• Week 5 (03/24, 03/26):

• 
  

Homework Assignments

Please submit your code (MATLAB/Python/C Language) and discussion report on eCourse2. You’re encouraged to work with classmates, but your report must be written independently. Any copying or plagiarism will be penalized. Discussing and comparing ideas is a good way to learn, use collaboration wisely. 

1. Write a program and investigate AR model for signals from different perspectives as many as you can.

2. Represent the data using deterministic bases such as the Hadamard, discrete sine, and discrete cosine bases. Additionally, explore data-dependent representations, including PCA and the Karhunen–Loève (KL) expansion. For simplicity, assume the data are zero-mean in the latter two cases. Compare your results and draw some conclusions from them.

References

1. C. E. Shannon, A Mathematical Theory of Communication, 1948. 

Additional Materials

Fun Readings

Pi-Day Artwork (Thanks for everyone's participation lol