PDF versionModule Leader
Lecturers
Prof S.S. Singh, Prof S. J. Godsill
Lab Leader
Prof S Godsill
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Study more advanced probability theory, leading into random process theory.
- Study random process theory and focus on discrete time methods.
- Introduce inferential methodology, including maximum likelihood and Bayesian procedures, and examples drawn from signal processing. Objectives
Objectives
As specific objectives, by the end of the course students should be able to:
- By the end of the course students should be familiar with the fundamental concepts of statistical signal processing, including random processes, probability, estimation and inference.
Content
Lectures 1-8: Advanced Probability and Random Processes
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Probability and random variables
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Sample space, events, probability measure, axioms.
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Conditional probability, probability chain rule, independence, Bayes rule.
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Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
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Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
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Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
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Random processes
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Definition of a random process, finite order densities.
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Markov chains.
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Auto-correlation functions.
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Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
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Ergodicity, Central limit theorem.
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Spectral density.
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Response of linear systems to stochastic inputs – time and frequency domain.
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Time series models: AR, MA, ARMA
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Lectures 9-16: Detection, Estimation and Inference
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Basic linear estimation theory: BLUE, MMSE, bias, variance
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Wiener filters
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Matched filters
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Least squares, maximum likelihood, Bayesian inference.
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The ML/Bayesian linear Gaussian model
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Maximum likelihood and Bayesian estimation
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Example inference models: frequency estimation, AR model, Estimation of parameters for discrete Markov chain.
Coursework
Random variables and random number generation
Learning objectives:
- Understand random variables and functions of random variables and their simulation
- To study the Jacobian as used with random variables
- To experiment with methods for non-uniform random number generation
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity involves preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
Last modified: 23/11/2022 08:40