SYLLABUS

Contact Information:

Time 8:00 to 8:50 AM MWF
Place CAVS classroom
Instructor Joseph Picone
Office: 2133 CAVS
Office Hours: by appt.
Email: picone@ece.msstate.edu
URL http://www.cavs.msstate.edu/research/isip/publications/courses/ece_7000_nonlinear
Required Textbook(s) Kantz and Schreiber Nonlinear Time Series Analysis, Cambridge, ISBN: 0-521-52902-6, 2004.
Prerequisite Familiarity with Linear Systems, Linear Signal Modeling techniques (e.g., Linear Prediction, Spectral analysis)
Reference Textbook(s) Henry D.I. Abarbanel, Analysis of Observed Chaotic Data, Springer, ISBN: 0387983724, 1997.

G.L. Baker and J.P. Gollub Chaotic Dynamics - an introduction, Cambridge, ISBN: 0-521-38258-0, 1990.

David Ruelle Chance and Chaos, Princeton University Press, ISBN: 0-691-08574-9, 1991.

S.J. Orfandis, Introduction to Signal Processing, Prentice-Hall, ISBN: 0-13-209172-0, 1996.

Grading Policies:

Final report 50%
Special assignments 25%
Lecture preparation 25%
Schedule:

The entries in the column labeled Section(s) refer to reading assignments in the course textbook.

Class Date Section(s) Scribe Topic(s)
01 01/20 Introduction SP,SR Introduction to Linear Signal Analysis techniques
02 01/20 Introduction SP,SR Dynamics of a system in the Phase Space
03 01/25 2 SL Review of Linear techniques-1
04 01/27 2 DM Review of Linear techniques-2
05 01/30 2 MP Phase Space Methods
06 02/01 3 SP Reconstructed Phase Spaces
07 02/03 4 SR Determinism and Predictability
08 02/06 4 - 4.3 JS Determinism and Predictability
09 02/08 4 SL Nonlinear Time Series Prediction
10 02/10 5 DM Lyapunov Exponents
11 02/13 -- Review Review of lectures 1 through 6
12 02/15 6 MP Correlation Integral and Dimensions
13 02/17 6 SP Correlation Dimension Estimation
13 02/17 6 SR Multi-scale and Self Similar Signals
15 02/22 6 JS Multi-scale and Self Similar Signals
16 02/24 7 SL Testing Nonlinearity with Surrogate Data
17 02/27 7 DM Testing Nonlinearity with Surrogate Data
18 03/01 8 MP Selected Nonlinear Phenomena - Bifurcation and Intermittency
19 03/03 8 SP Selected Nonlinear Phenomena - Quasi-periodicity
20 03/06 9 SR Advanced Embedding Methods
21 03/08 9 JS Advanced Embedding Methods
22 03/20 9 SL Advanced Embedding Methods
23 03/22 9.4-9.6 DM Fluctuating Time intervals
25 03/24 4.4.3, 8.3 MP TBD
26 03/27 8.4 SP SVD Embedding
27 03/29 10 SR Local Projective noise Reduction
28 03/31 10 JS Local Projective noise Reduction
30 04/03 11.1 SL Ergodicity and strange attractors
31 04/05 TBD DM Estimating Correlation integral from a time series
32 04/07 TBD MP Correlation Dimension
33 04/10 TBD SP TBD
34 04/12 TBD SR TBD
35 04/17 12.2-12.4 JS TBD
36 04/19 12.5-12.7.3 SL Overfitting and model Verification
37 04/21 TBD DM TBD
38 04/24 TBD MP TBD
39 04/26 TBD SP TBD
40 04/28 TBD SR TBD
41 05/01 -- JS Review of chapter 8
42 05/03 -- Review Review of lectures and discuss term paper
43 05/05 Cumulative TBD Final report