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ECE551

ECE551 (Digital Signal Processing II) is a 4-credit-hour graduate course. It is offered in the fall only.

Content Covered

  • All-Pass Systems and Minimum-Phase Systems
  • Group Delay and Minimum Energy Delay
  • Signal Modelling and System Identification
  • Pade's, Prony's, Shank's Methods
  • Linear Predictive Modelling
  • Multichannel Sampling by Papoulis
  • Digital Rate Conversion
  • Multi-rate Signal Processing
  • Noble Identities and Polyphase Representation
  • Multi-rate Digital Filter Bank
  • 2-Channel Multi-rate Filter Bank
  • Quadrature Mirror Filters (QMF)
  • Conjugate Quadrature Filters (CQF)
  • Time-frequency analysis and Uncertainty
  • Window Fourier transform (STFT and Wavelet Transform)
  • Wavelet Transform
  • Harr wavelet Design and Daubechies wavelets
  • Random Signals
  • ARMR Model
  • Yule-Walker Equation
  • Levinson-Durbin Algorithm and Lattice Structure
  • Direct Form I, Direct Form II and Lattice Form
  • Optimal Forward / Backward Linear Prediction
  • Adaptive Filtering: Wiener Filter and Its Applications
  • LMS Algorithm by Bernard Widrow
  • SVD-Based Linear Predictive Modelling
  • PCA, ICA, CCA

This course goes over a wide list of specific signal processing topics that are loosely to relatively related. The course starts out with review of ECE310 topics sepcifically LTIC. The course then splits off into different specialized subtopics in signal processing. This course heavily goes into the proofs of those concepts and the history behind where they arise from. It is quite hypothetical in framework and mostly focuses on how modern signal processing has gotten to this state. The course provides a swiss army knife of skills for those going into signal processing.

Prerequisites

ECE310 is an official prerequisite of the class as it is the needed to understand topics such as LTIC, up/down sampling, and A/D and D/A systems which are the basis for more advanced topics.

ECE313 is an official prerequisite of this class since noise in signals is introduced in this class.

  • [ECE534] (ECE534.md)

While [ECE534] (ECE534.md) is not an official prerequisite it is quite useful for understanding concepts such as autocorrelation that come up in class quite often.

When to Take it

Take this course if you have a high interest in digital signal processing (DSP). DSP is also important in fields such as control systems, computer vision, and machine learning. This course is for those who know they strongly want to study or research signal processing.

Course Structure

This course has around weekly homeworks, two midterms, and one final.

As of Fall 2025, this course's midterms and final questions are not the most difficult as quite a few question come from homework directly or are slightly altered.

The homeworks are quite difficult and require students to read the textbook to understand and ingest the material a bit more than just lecture does.

Instructors

Professor Liang has taught this course for 3 years. He really enjoys discussing the big picture of where each concept fits in the signal processing schema. Lectures are not recorded and only doen on the blackboard, so lecture is essentially required.

Course Tips

Go to lecture for this course and read the textbooks. Liang teaches quite fast and goes over many topics so being able to take notes is essential. Homeworks are extremely useful for doing well on tests, so do the homework!!

Life After

Student after taking this course will most likely go into industry in signal processing for do research in the field.

Infamous Topics

  • Linear prediction is quite a struggle and understanding the nuances between how each of the methods work is difficult.
  • Yule-Walker and Levinson-Durbin are not too difficult in themselves, but applying them in signal processing gets very heavy in the math which can be seen are qutie difficult.

Resources

This textbook quite helpful in understanding this class. - A.V. Oppenheim, R.W. Shafer, and J. R. Buck, Discrete-Time Signal Processing, Prentice-Hall, 1999