Course Outline
Description
Introductory graduate level course in statistical signal processing. This course
focuses on the roles---good and bad---that stochastic signals play. Some interesting
signals---neural signals for one---are by their very nature stochastic. An example
of a "bad" random signal is noise. Statistical signal processing develops optimal
algorithms to extract information from or in the presence of stochastic signals.
All of these algorithms hinge on
fundamental results in
estimation and
detection.
Prerequisites: Knowledge of stochastic processes and probability.
- Review
Probability, stochastic processes, and optimization theory.
- Estimation Theory
- Terminology
- Parameter estimation: MMSE, maximum a posteriori, linear estimates, maximum
likelihood, Cramér-Rao
theory
- Signal parameter estimation:
Linear and nonlinear estimation techniques
- Signal waveform estimation:
Wiener filters, Kalman filters, adaptive
filters
- Spectral estimation
- Statistical Hypothesis Testing
- Optimality criteria and the likelihood ratio test
- Consistency tests
- Sequential tests
- Unknown parameters (composite tests)
- Links to estimation theory
- Discrete-Time Detection Theory
- Detection of signals in additive Gaussian noise
- Detection in the presence of certainties: unknown signal and noise parameters, unknown
signal waveforms. CFAR detection.
Course material
- D.H. Johnson. Estimation & Detection Theory.
Available as a coursepak at the Rice Campus Store.
Don H. Johnson
11.08.2006