The course "The Signal Theory" will provide a deeper look into stochastic and deterministic signals, in particular their characterization and their approximation. Signals with specific structure (e.g., signal spanned by only a few basis functions; sparse signals) will be covered.

Part I: Stochastic Signals

• The Concept of Stochastic Processes
  basic concepts; characteristic quantities; complex processes (equivalent baseband signals)
• Spectral Representation and Spectral Estimation
  innovations; Fourier and Karhunen-Loeve expansion; spectral estimation / periodogram; parameter estimation
• Mean-Square Estimation
  prediction and filtering; unbiased estimation; Cramer-Rao bound

Part II: Deterministic Signals

• Approximation of Signals
  sampling and equivalent sequences; series expansion; signal spaces and bases; signals with structure / low-dimensional bases; compressed sensing
• Localization and Uncertainty
  time-frequency plane; local (short-time) Fourier Spectrum / Wavelets