C8421 - TIME SERIES ANALYSIS AND SIGNAL PROCESSING

Learning outcomes

At the end of the course, students acquire theoretical, computational, and applied skills that prepare them for working with any time-dependent signal produced by the atmosphere, oceans and the solid Earth, as well as in communications or information systems.

Course contents

Time Series Analysis and Signal Processing represent the most common methods for understanding temporal data and models in science and engineering. The study of physical processes relies heavily on these tools and the underlying statistics, enabling analysis across timescales ranging from microseconds to millions of years. Furthermore, signal theory serves as an ideal introduction to statistical methods for hazard assessment—relevant across all fields of Earth Physics—as it is essential for anomaly detection and forecasting.

The course is structured to build foundational knowledge in correlation, frequency transformation, and convolution analysis—techniques with broad applicability to time series analysis. Building on these concepts, the course explores applications using real-world data from atmospheric physics, oceanography, and solid-earth physics, giving students practical experience with the analytical methods commonly used in research.

Students are expected to have a solid prior understanding of the mathematical methods fundamental to physics. The topics covered provide the skills necessary for professional work in meteorology, geophysics, and applied physics, particularly within research institutes and companies focused on resource and risk assessment.

The course includes computational exercises designed to provide students with initial training in the software and programming languages used by the scientific and engineering communities for signal processing.

Topics

 Time series analysis: Time series as a mathematical and physical tool for studying oscillatory phenomena.

Signal processing: Design of temporal filters and their application to time series describing physical processes.
Computational processing: Advanced time series processing using open-access software and advanced correlation theories.

Visualization and interpretation: Collaborative coding, 3D and 4D visualization of geophysical data, and interpretation of physical data.

Readings/Bibliography

- D. Gubbins, Time Series Analysis and Inverse Theory, Cambride University Press, Cambridge UK, 2004.

- A. I. Vistnes, Physics of Oscillations and Waves With use of Matlab and Python. Springer, 2018.

- R. E. Thomson & W. J. Emery, Data Analysis Methods in Physical Oceanography, 2024.

- R. H. Shumway & D. S. Stoffer, D. S. Time series analysis and its applications: With R examples (4th ed.). Springer., 2017.

Teaching methods

Each lecture is accompanied by a PowerPoint presentation. The collection of files, organized by chapter, provides a comprehensive overview of the syllabus and can serve as a study resource for the subject. These PowerPoint files are made available throughout the course and can be accessed via the course webpage.

The course includes computer-based practical sessions involving programming in Julia, Matlab, and Python; active participation from attending students is expected during these sessions. In the course of these sessions, students will download data from online providers and demonstrate their understanding of the techniques taught by applying them to examples relevant to their specific field of interest.

Assessment methods

The exam will be oral and last approximately 30 minutes.

The student will be asked to present three topics covered during the course, one after another. For each topic, the student will first be asked to outline the general context, followed by a discussion of specific details.

Answers will be evaluated based on depth and accuracy, taking into account practical and computational learning.

The final grade will be the arithmetic mean of the scores obtained for each question.

Teaching tools

The course uses Power Point files that will have connections to online resources, such as seismological databases and codes, which will contribute to the student's computational and data training.

The exercises include instructions given in advance for installing codes and downloading datasets on a personal computer, for in-class exercises and, optionally, outside of course time.

Office hours

See the website of Luca De Siena