The course "The Signal Theory" will provide a deeper look into stochastic and deterministic signals, in particular their characterization and estimation. Signals with specific structure, in particular topics in sampling and reconstruction and Compressed Sensing are covered.

Part I: Stochastic Signals

• Random Variables
• Estimation
• Stochastic Processes
• Mean-Square Estimation and Ergodicity

Part II: Deterministic Signals

• Sampling and Interpolation
• Compressed Sensing

Stochastic Processes / Detection

• A. Papoulis, S.U. Pillai. Probability, Random Variables and Stochastic Processes. McGraw-Hill, New York, 4th edition, 2002
• H.L. Van Trees. Detection, Estimation, and Modulation Theory, Part III: Radar-Sonar Signal Processing and Gaussian Signals in Noise. John Wiley & Sons Inc., 2001.
• R.G. Gallager. Stochastic Prosesses: Theory for Applications. Cambridge University Press, 2013.
• B. Hajek. Random Prosesses for Engineers. Cambridge University Press, 2015.

Digital Signal Processing / Compressed Sensing

• M. Vetterli, J. Kovacevic, V.K. Goyal. Foundations of Signal Prosessing. Cambridge University Press, 2014.
• Y.C. Eldar. Sampling Theory: Beyond Bandlinited Systems. Cambridge University Press, 2015.
• Y.C. Eldar, G. Kutyniok (editors). Compressed Sensing: Theory and Applications. Cambridge University Press, 2012.
• K.-D. Kammeyer, K. Kroschel. Digitale Signalverarbeitung: Filterung und Spektralanalyse. Springer Vieweg, 8. Auflage, 2012.

• Exercise No. 1 (Basics of RV - Part I.)
• Exercise No. 2 and 3 (Basics of RV - Part II, Two RV , and Functions of RV.)
• Exercise No. 4 (Estimation I)
• Exercise No. 5 (Estimation II)
• Exercise No. 6 (Stochastic Processes I)
• Exercise No. 7 (Innovation)
• Exercise No. 8 (MS Estimation & Spectral Estimation)
• Exercise No. 9 (MS Estimation & Ergodicity)
• Exercise No. 10 (Sampling and Reconstruction I)
• Exercise No. 11 (Sampling and Reconstruction II)
• Exercise No. 12, refer to Announcements.