מידע כללי General Information Общая Информация معلومات عامة

Introduction 

This course introduces fundamental methods for representing, processing, and analyzing data using deterministic and probabilistic tools. It provides a foundation for advanced topics such as deep learning and convolutional neural networks.

The course covers the digitization of signals and data, their representation in different bases, and the efficient use of these representations in signal processing. Topics include sampling and quantization, bit allocation, Fourier representations and their optimality, functional maps, convolution, compression, dimensionality reduction, principal component analysis (PCA), and filtering methods for restoring blurred or noisy data. Signals and systems are studied in both continuous and discrete settings.

The course carries 3 credit points. Lectures and tutorials may be delivered in English upon request.

Prerequisites

The course requires a solid background in linear algebra, calculus, and probability, as well as basic knowledge of differential equations. Formally, Numerical Algorithms (02340125) or an equivalent course should be sufficient.

Homework 

Homework assignments will be published approximately every four weeks, subject to change. Assignments will include theoretical and programming questions.

Theoretical solutions must include rigorous proofs written in English. Programming assignments must be completed in Python.

All homework assignments must be submitted in pairs.