CE-S 690
INSTRUCTOR
Prof. Athina Petropulu Rm. 7-221, Tel. x2358, e-mail: athina@artemis.ece.drexel.edu
Office Hours: Wed. 1:00-2:00 or by appointment
CLASS SCHEDULE
Thursday 6-9, Rm. *** (the time/date can be changed to
accommodate the majority of interested students)
PREREQUISITE
ECE- 631, ECE-S 632, Stochastic Processes, Strong math background
TEXTBOOK
Class Notes
REFERENCES
G.W. Wornell, ``Signal Processing with Fractals a wavelet-based approach",
Prentice Hall, 1996.
G. Samorodnitsky and M.S. Taqqu, ``Stable non-Gaussian random processes,"
Chapman and Hall, 1994.
C.L. Nikias and M. Shao, ``Signal Processing with alpha-stable distributions
and applications," John Wiley & Sons, Inc., 1995.
COURSE DESCRIPTION
The goal of this new course is to cover the state-of-the art as well as the basics in the ``hot" area of self-similar processes and a-stable processes. Self-similar processes abound in nature; a partial list includes economic time series, biological signals, electromagnetic fluctuations, electronic device noises, internet traffic, etc. Such signals exhibit long-range dependence, thus conventional models do not apply.
a-stable distributions (0 < a < 2) can be viewed as generalization of Gaussian distributions, and include the Gaussian one as a limiting case (a =2). The main difference between the stable and the Gaussian distributions is that the tails of the stable density are heavier, which is evidence of impulsive time domain behavior. The parameter a represents the heaviness of the density tails. Such distributions have been well known for their lack of second- and higher-order moments. The result of a large number of spatially and temporally distributed sources that produce random signals of short duration follows an a-stable model. Thus, a-stable distributions can be used to model radar returns, ultrasound echoes, etc. Other applications include interference modeling in wireless communication systems, economic time series, noise in power lines, etc.
To capture both data burstiness and long-range dependence of data, a-stable self-similar processes, such as linear fractional stable noise or fractional Levy stable motion, have been proposed in cases such as modeling network traffic, infrared scene modeling, heart-bit interval increments, etc.
The course targets audience (both students and faculty) who do research
in signal modeling/analysis and are looking for new mathematical tools.
As the potential applications of such signals are endless, limited amount
of time will be spent on specific applications. The focus of the course
will be on in-depth study of the underlying mathematical framework, identifying
the state-of-the art in the respective fields, and pointing out open problems.
Coming out of the course one should be able to apply effectively
these tools in their research, and maximize the potential of innovative/publishable
results.
GRADING POLICY
Grade will be determined based on a paper presentation (70%), and on class participation (30%).
A list of IEEE Transactions papers will be provided by the instructor for the students to choose. Presentations will be held in class, during the last 30-45 minutes of the weekly lecture (estimated frequency: one presentation per week).
Homework will also be assigned. Although it will not count towards the final grade, it may help resolve border-line cases.
TENTATIVE COURSE OUTLINE
- Statistically self-similar signals
- Estimation of 1 / f signals
- Linear self-similar systems
- Stable distributions
- Symmetric a-stable models for impulsive noise
- a-stable self-similar processes
1 / f processes; fractional Brownian motion; fractional Gaussian noise; nearly 1 / f signals.
parameter estimation; smoothing.
linear time invariant systems; linear scale invariant systems.
characteristic function; generation of stable random variates; symmetric stable distributions; parameter estimation; fractional order moments.
filtered Poisson processes; detection in stable noise.
a-stable Levy motion; fractional stable noise.