Adaptive Signal Processing
Subject code: SIP 7024
Lecturer
Prof Doug Gray
University of Adelaide
Mode of delivery
On-line with possibility of 3-5 day short course or weekly
lecture delivery.
Assumed knowledge
Linear algebra (matrices), basic ideas of probability theory and statistics
(consider taking Detection, Estimation and Classification course),
basic concepts of
linear systems, for example, impulse response, transfer functions, Fourier and
z-transforms (consider taking Introduction to Discrete Linear Systems course), MATLAB.
Aim/Learning Objectives
This subject is strongly mathematics based and it's principal aim is to teach
students the fundamental mathematical principles underlying the subject.
Equally important is to impart to students the ability to apply such
mathematical principles to data through the processing of actual signals. The
subject is specifically structured around these aims.
On successful completion of the course students will
- have sufficient grasp of the basic mathematical principles of random processes, optimum and adaptive filtering to enable them to understand research literature on this subject
- be able to design optimum and adaptive linear filters for application to noisy time series data.
- be able to implement algorithms in MATLAB and to understand and interpret results obtained.
In practice it is not always obvious how a particular filtering problem may be
able to be solved using the methods introduced in the lectures. Often very
useful techniques can be developed by reinterpreting what is signal and what is
noise. This is where your skills and ingenuity can be
used -- the better your
understanding of the basic principles the better the solutions you will be able
to come up with.
Content
After some introductory material the course splits into
the four main areas listed below.
Statistical Signal Processing
Random variables
Random processes
Covariance matrices
Optimum Filters
Wiener filters
Matched filter
Minimum mean square error - discrete
Constrained optimisation
Method of steepest descent - convergence issues
Adaptive Filters
Stochastic gradient descent - convergence in mean and misadjustment
Recursive least squares and vector space approaches
Linear prediction
Levinson-Durbin
Lattice filters
Applications of linear prediction
Finally some case studies and extension topics will
briefly be visited and not all of the above topics may be covered.
Assessment
It will generally be 50% assignments (5), 25% examination,
25% quizzes, however these percentages are indicative only
and may be varied at the lecturer's discretion.
Details of the actual assessment used in a given year
can be found in the study guide provided at the start of the semester.
Resources
The material is presented within a rigorous mathematical framework although the
notational details have been kept to a minimum as much as possible. A
comprehensive set of lecture notes are provided but not all of these will be
covered in class and students are expected to do their own reading out of
session. Lectures will focus on concepts, applications and practical
implementation issues rather than rigorous mathematical proofs although
students are expected to master these as well. Many of the assignments and
tutorials are focussed on the application of the theory covered in lectures to
data and the course standard of MATLAB has been chosen for this.
Most material is available on the web and any additional material will
be emailed to students during the course.