PhD Courses in Denmark

Description: Spectral analysis is a fundamenal tool in a broad range of scientific disciplines, including telecommunications, chemistry, power electronics, and speech and audio processing. The course gives an overview of modern methods for spectral analysis for both stochastic and deterministic signals, including both parametric and non-parametric methods. More specifically, a number of methods based on different principles will be discussed, namely classical methods based on the Fourier transform, methods based on concepts from linear algebra such as shift-invariance and subspaces, optimal distortion-less filtering methods, and sparsity-based methods based on convex optimization and statistical principles. The properties of these methods will be analyzed and their application to real signal will be discussed.

Prerequisites: Basic probability theory, linear algebra, signal processing, and experience with MATLAB and/or Python programming.

Learning objectives: 

1. Develop a deep understanding of the theoretical foundations of spectral analysis, including the distinction between stochastic and deterministic signals.

2. Gain proficiency in both classical methods based on the Fourier transform and modern techniques that leverage linear algebra, such as shift-invariance and subspace methods.

3. Differentiate between parametric and non-parametric methods for spectral analysis, and assess the advantages and limitations of each approach in various scientific applications.

4. Master the principles and applications of optimal distortion-less filtering methods in spectral analysis, and understand their significance in reducing noise and enhancing signal clarity.

5. Learn and apply sparsity-based methods, grounded in convex optimization and statistical principles, to effectively analyze sparse signals.

6. Critically evaluate the performance of different spectral analysis techniques, considering factors such as accuracy, computational efficiency, and robustness.

7. Develop the ability to apply various spectral analysis methods to real signals within the students problem domain.

8. Keep abreast of the latest advancements in spectral analysis methods and their applications, fostering the ability to adapt to emerging challenges and innovations in the field.

9. Prepare to conduct independent research in the field of spectral analysis, contributing to the development of new methods or the novel application of existing techniques to solve complex scientific problems.

Organizer: Jesper Rindom Jensen

Lecturers: TBA

ECTS: 3.0

Time: 25, 26, 27, 28, 29 August 2025

Place: Aalborg University (Room: TBA)

Zip code: 9220

City: Aalborg

Maximal number of participants: 15

Deadline: 4 August 2025