052600 VU Signal and Image Processing (2025W)

Algorithms for data analysis are often based on the assumption of independent and identically distributed (i.i.d) data. The world, however, often violates the first "i", i.e., it generates data with a rich spatial and temporal structure such as time-series and images. Representing, understanding, and processing this structure is the domain of signal processing. As such, a firm grasp of signal processing is essential to understand structure in data and design systems that exploit this structure.

In the first part of this course, we will approach signal processing from the perspective of linear time-invariant (LTI) systems, i.e., we will consider signals as outputs of LTI-systems [1]. This approach will lead us to study the discrete(-time) Fourier transform (D(T)FT) and its applications, including sampling and filter design. In the second part of the course, we will study several variants and extensions of the Fourier transform, including the Hilbert-, Discrete Cosine- and Wavelet transforms. In the third part of the course, we will take an alternative approach to signal processing and consider signals as realizations of stationary stochastic processes [2]. This will lead us to the field of stochastic spectral analysis. We will conclude the course with an introduction to information theory and compression algorithms, e.g., the Lempel-Ziv-Welch (LZW) algorithm that is used in data formats such as ZIP and TIFF.