Supervisors:

• Prof. Marta Molinas: Course Responsible and main lecturer
• Prof. Olav Bjarte Fosso: Lecture on EMD Mode Mixing problem
• Dr Andres Soler: Lecture on Wavelets

Digital Signal Processing, Mathematics 4 (Math 4K), Object Oriented Programming or equivalent. Require knowledge about Matlab or Python.

The objective of this course it to gain a better understanding of classical data analysis and adaptive data analysis methods, with a focus on their applicability to data from complex systems.

Data are the direct record of an event, such as rocket launch, a phenomenon, nature, music or engineering process. The record can be taken by our eyes, ears, electronic sensors, or mechanical devices. We analyze the data, detect signals and make decisions or design controllers with the information obtained. Data are thus the connection between the reality and us and data analysis is for us to understand the reality and to find out its underlaying driving mechanism. In this sense, data analysis is very different from data processing. Data analysis emphasizes detailed decomposition and examination of the data to extract physical understanding, while data processing often relies on established algorithms and machines to output values of mathematical parameters.

Data from a complex nature cannot be represented by a priori basis, when looking for physical meaning. Examples of such data comes from biological systems (EEG, ECG, EMG, stock markets, the rain, music, birds songs, speech, etc. To analyze these, we need adaptive data analysis methods that can capture the nonlinear and non-stationary properties of the system and the data. This course will examine the advantages and disadvantages of a priori and adaptive data analysis methods, by implemetning them when using real data from various processes and systems, adn by performing time-frequency analysis methods and spectral analysis. Examples of implementation will use Short-Time Fourier transform, Wavelet transforms, Hilbert-Huang transform, Bayesian methods, Kalman filtering. etc. In the implemetnations, emphasis will be put on the understanding of time-frequency concept and the related uncertainty principle.

The course assignments will consist on group-work (2 students per group)and two main tasks per group, where two types of data-sets (one synthetic data-set and one real data-set) will be analyzed by using two approaches: one based on adaptivity and one based on a priori models. The representations extracted from both methods will be compared and discussed aiming at a physical interpretations when applicable. For the work-group with real data-set students should bring the real-data connected with their current research project and they will work on those data.

Oral exam – 20 min examination on a paper written by the student-pair where a given data analysis technique/s is used.