Foundations of Signals and Systems

Computational Imaging

The students are able to understand modern imaging techniques, i.e. combined hardware/software imaging solutions which implies a good comprehension of both, their hardware properties and their software implementations. For this, the students improve their understanding of, on the one hand, optical and sensor properties as well as hardware-based modulation approaches, and, on the other hand, the mathematical modeling and solution strategies for the ensuing algorithmic treatment of the data generated by the computational imaging device. Overall, the students are enabled to understand and apply state-of-the-art computational imaging technology, forming the basis for research in the subject area.

Signals and Systems II

This course continues “Signals and Systems I” (formerly Communications Engineering I) Provision of mathematical and telecommunications fundamentals, skills and abilities. Proficiency: • 2D: basics of optical imaging and characterization of imperfections • Modelling of optical systems with Fourier Optics, assessment of approximation error • Performance measures of optical systems • Sampling and reconstruction in 2D, noise characteristics of digital sensors, aliasing • Multi-dimensional convolution and Fourier transform • Multi-dimensional sampling (• 3D: Tomography • Radon transformation, Fourier Slice Theorem • 4D: Light Field and Computational Imaging) Skills: • Application of signal-theoretic concepts to optical and other imaging systems • Multidimensional signal processing in the time/spatial domain • Description and analysis of space-variant systems • Generalization capability to higher dimensions and other settings than 1D time-domain signal processing Competences: Application of linear system theory for the development of processing algorithms in multidimensional signal processing (coding theory, image processing, image analysis)

Signals and Systems I

Signals and Systems

This lecture gives electrical engineering and computer science students useful tools and an understanding of signals, their properties, and behavior after being manipulated by different types of systems.

Synthetic Aperture Radar & SAR Interferometry

SAR stands for Synthetic Aperture Radar. This imaging radar method has established itself in recent years as an indispensable imaging method in remote sensing of the earth, especially in the field of environmental observation.

The student will learn the basics of how to use the principle of synthetic aperture to improve the geometric resolving power and thus how to use radar sensors for image acquisition. The influences of waveform, wavelength, antenna, acquisition geometry and the properties of the scene on the obtained radar image are presented and explained to the students.

The knowledge gained is applied by processing real radar data.


Knowledge of signals and systems  (SiSy I+ II) is desired but not required.


Grundlagen der Signal- und Systemtheorie

Das Modul "Grundlagen der Signal- und Systemtheorie" vermittelt die Grundlagen zur Beschreibung von Signalen und linearen Systemen. Ausgehend von der Beschreibung periodischer Signale durch Fourier-Reihen wird die Fourier-Transformation für beliebige Signale eingeführt. Im gleichen Kontext wird die Beschreibung linearer, zeitinvarianter Systeme behandelt. Nach der Überleitung der Fourier-Transformation in die Laplace-Transformation werden zur Beschreibung von Signalen und Systemen verallgemeinerte Funktionen eingeführt und deren Bildfunktionen abgeleitet. Die Z-Transformation schließt den Bereich Signaltheorie ab. Im letzten Kapitel des Moduls wird die Beschreibung linearer Systeme behandelt. Die Inhalte gliedern sich in:

  • Elementarsignale
  • LTI Systeme
  • Faltung
  •  Fourier Transformation, inkl. DFT/FFT
    • Fourierreihen, reel, komplex, kontinuierliche Transformation
    • Sampling Theorie
  • Laplace Transformation, inkl. z-Transf.
    • Zweiseitig / einseitig (kausale Systeme)
    • Mathematische Beschreibung von Differentialgleichungen höherer Ordnung durch Systeme von Differentialgleichungen erster Ordnung
    • Lösung von ODEs / Systemen von ODEs 
  • Optional: Generelle Integralinformationen