SIGNAL PROCESSING

This course offers an introductory module designed for PhD students in Computer Science with diverse academic backgrounds. The course provides essential conceptual and mathematical tools from signal processing, creating an explicit bridge between classical signal theory (LTI filters, frequency-domain analysis, sampling theorem, stochastic modeling, and estimation) and modern machine learning/deep learning paradigms (convolutional neural networks, autoencoders, etc.)

Upon successful completion of the course, students will be able to:

- Understand and apply fundamental principles of time- and frequency-domain signal analysis (Fourier transform, Nyquist-Shannon sampling theorem, aliasing phenomena).
- Interpret the mathematical and conceptual connections between classical discrete filtering and modern deep learning layers (e.g., convolutional layers in PyTorch/TensorFlow).
- Grasp core paradigms in compressive sensing, stochastic time-series forecasting (ARMA), and state-space estimation (Kalman filtering).
- Critically evaluate the strengths and synergies between classical techniques and neural/generative approaches for signal restoration, denoising, and feature extraction from sensor or sequential data.

Basic knowledge of linear algebra, calculus, and probability theory at the Master's level in Computer Science or related STEM disciplines. Prior expertise in signal processing or advanced machine learning is not strictly required.

The course is structured into 5 lectures of 2 hours each:
1. Time Domain: Continuous and discrete-time signals, Linear Time-Invariant (LTI) systems, convolution sum, and the conceptual bridge to Deep Learning convolutional layers.
2. Frequency Domain: Fourier Transform, Fast Fourier Transform (FFT), STFT, and spectrograms. Nyquist-Shannon sampling theorem, frequency-domain aliasing, and classical filtering.
3. Underdetermined Systems & Compressive Sensing: L_0, L_1, L_2 norms, signal sparsity, and reconstruction via optimization (Lasso / Basis Pursuit).
4. Stochastic View & Time Series: Random processes, stationarity, ARMA forecasting, state-space models, and the Kalman filter compared with recurrent neural architectures (RNN/LSTM).
5. Signal Restoration: Inverse problems, Wiener filtering, and classical deconvolution. Transition to Autoencoders and Variational Autoencoders (VAEs) for non-linear signal denoising and synthesis.

[1] Oppenheim, and Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989. Print.
[2] Smith, Steven W. The scientist and engineer's guide to digital signal processing. 1997. [online: http://dspguide.com ]

Students will complete a short project work (individually or in small groups) focusing on an in-depth study or practical application (via theoretical analysis or code implementation) of one or more topics covered during the course.

oral

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

27–30 cum laude: Excellent understanding and mastery of all course topics, combined with outstanding critical analysis and autonomous application in the project work.
23–26: Good understanding of core concepts and correct application of methodologies in the submitted project.
18–22: Sufficient understanding of basic course concepts with limited depth of independent analysis.

Interactive lectures covering theoretical and conceptual foundations, complemented by Python code demonstrations (using SciPy/PyTorch) to illustrate the practical application of classical SP and ML operations