Description
Linear and nonlinear signal analysis. Introduction to the theoretical concepts and application to different classes of signals.

Objectives
Linear and nonlinear signal analysis allows one to characterize dynamical systems by means of the analysis of signals measured from these dynamics. The course will give an introduction to the most important techniques and algorithms in linear and nonlinear signal analysis. In the theoretical part the underlying concepts will be introduced, and in the practical part applications to various kinds of signals will be carried out.
The course does not require any pre-knowledge about signal analysis.
The course will be held in English

Sylabus

- Power spectrum and autocorrelation function
- Statistical moments
- Delay embedding
- Nonlinear prediction error
- Lyapunov exponents
- Correlation dimension
- The concept of surrogates

Organization
In the theoretical part the underlying concepts will be introduced. In the practical part applications to various kinds of signals will be carried out.

Practice
The participants will be instructed and supervised to apply the techniques introduced in the theoretical part to various kinds of signals. The participants will be encouraged to bring their own small set of signals. These could signals which can be downloaded from the internet such as long records of stockmarket values, climate data, or physiological recordings such as an electrocardiogram. These could also be signals from other projects of the participants. The progress in these applications will be used to evaluate the participants’ work (60%, see below). All applications will be carried using the Matlab or Octave software. Also here, no pre-knowledge is required.

Evaluation Methode
Final Exam (40%) and practice (60%)

Basic bibliography
Holger Kantz and Thomas Schreiber, "Nonlinear time series analysis, Cambridge University Press, Cambridge 1997.

Complementary bibliography
T. Schreiber Interdisciplinary application of nonlinear time series methods. Phys. Rep. 308, 2 (1999).
This article can be downloaded for free at: http://xxx.lanl.gov/PS_cache/chao-dyn/pdf/9807/9807001.pdf