phy731 Compulsory Optional Subject Theory (Complete module description)

Bachelor in Physik, Technik und Medizin oder entsprechender Abschluss

Digital Signal Processing Grundlagen der diskreten und integralen Signalrepräsentation (Eigenfunktionen), Abtastung, Signaltransformationen (Fourier-Transformation, Diskrete Fourier-Transformation, FFT, z-Transformation), Systemeigenschaften (Linearität, Zeitinvarianz, Stabilität, Kausalität), Methoden zur Beschreibung und Analyse von digitalen Systemen im Zeit- und Frequenzbereich (Impulsantwort, Übertragungsfunktion), stochastische Prozesse und lineare Systeme, digitale Filter, Optimalfilter, Adaptive Filter im Zeit- und Frequenzbereich.
Machine Learning II - Advanced Learning and Inference: This course builds up on the basic models and methods introduced in introductory Machine Learning lectures. Advanced Machine Learning models will be introduced alongside methods for efficient parameter optimization. Analytical approximations for computationally intractable models will be defined and discussed as well as stochastic (Monte Carlo) approximations. Advantages of different approximations will be contrasted with their potential disadvantages. Advanced models in the lecture will include models for clustering, classification, recognition, denoising, compression, dimensionality reduction, deep learning, tracking etc. Typical application domains will be general pattern recognition, computational neuroscience and sensory data models including computer hearing and computer vision. Processing and analysis of biomedical data Normal distributions and significance testing, Monte-Carlo bootstrap techniques, Linear regression, Correlation, Signal-to-noise estimation, Principal component analysis, Confidence intervals, Dipole source analysis, Analysis of variance. Each technique is explained, tested and discussed in the exercises.

- B. Girod, R. Rabenstein, A. Stenger, Signals and Systems, Wiley, 2001.
- J. G. Proakis, D. G. Manolakis, Digital Signal Processing – Principles, Algorithms and Applications, Prentice
   Hall, 2007.
-  A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, 2009.
- S. Haykin, Adaptive Filter Theory, Prentice Hall, 2001.
- C. M. Bishop, Pattern Recognition and Machine Learning, Springer 2006 (best suited for lecture).
- K. P. Murphy, Machine Learning: A Probabilistic Perspective, MIT Press, 2012.
- D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, 2003
  (free online)
- K. Petersen, M. Pederson, The Matrix Cookbook, (free online) 
- Kirkwood B.R. and Sterne A.C., Essential Medical Statistics: 2nd editition. Blackwell Science. Oxford,
   2003
- Cho, Z.H. and Singh J. P. J. M.: Foundations of Medical Imaging. John Wiley, New York, 1993
- Kutz, J.N. Data-Driven Modeling and Scientific Computation: Methods for complex systems and Big Data.
  Oxford University Press, Oxford, 2013