| 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. |
| Final report | 50% |
| Special assignments | 25% |
| Lecture preparation | 25% |
| 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 |