Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2020-21
Module Leader
Lecturers
Dr S.S. Singh, Prof S. J. Godsill
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Prerequisites
3F1
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 28/08/2020 11:06
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2023-24
Module Leader
Lecturers
Prof A Guillen i Fabregas, Prof S. J. Godsill
Lab Leader
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 05/01/2024 12:25
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2024-25
Module Leader
Lecturers
Prof S. J. Godsill, Dr G Cantwell
Lab Leader
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 31/05/2024 09:54
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2019-20
Module Leader
Lecturers
Dr S.S. Singh, Prof S. J. Godsill
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Prerequisites
3F1
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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 see the Booklist for Part IIA Courses for references for this module.
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 23/09/2019 14:25
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2025-26
Module Leader
Lecturers
Prof S. J. Godsill, Dr G Cantwell
Lab Leader
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/06/2025 13:21
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2021-22
Module Leader
Lecturers
Dr S.S. Singh, Prof S. J. Godsill
Lab Leader
Prof S Godsill
Timing and Structure
Michaelmas term. 16 lectures.
Prerequisites
3F1
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 20/05/2021 07:39
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2017-18
Module Leader
Lecturers
Prof S Godsill and Dr S.S. Singh
Lab Leader
Prof S Godsill
Timing and Structure
Michaelmas term. 16 lectures.
Prerequisites
3F1
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic Linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Model choice (AIC, BIC, Bayesian) and Bayes decision theory
-
Maximum likelihood and Bayesian detector (cf matched filter)
-
Example inference models: frequency estimation, AR model, Estimation of parameters for discrete Markov chain.
Coursework
[Coursework Title]
Learning objectives:
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity [involves/doesn't involve] preliminary work ([estimated duration]).
Full Technical Report:
Students [will/won't] have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 03/08/2017 15:40
Engineering Tripos Part IIA, 3F3: Statistical Signal Processing, 2018-19
Module Leader
Lecturers
Dr S.S. Singh
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Prerequisites
3F1
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
-
Probability and random variables
-
Sample space, events, probability measure, axioms.
-
Conditional probability, probability chain rule, independence, Bayes rule.
-
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
-
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
-
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
-
-
Random processes
-
Definition of a random process, finite order densities.
-
Markov chains.
-
Auto-correlation functions.
-
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
-
Ergodicity, Central limit theorem.
-
Spectral density.
-
Response of linear systems to stochastic inputs – time and frequency domain.
-
Time series models: AR, MA, ARMA
-
Lectures 9-16: Detection, Estimation and Inference
-
Basic linear estimation theory: BLUE, MMSE, bias, variance
-
Wiener filters
-
Matched filters
-
Least squares, maximum likelihood, Bayesian inference.
-
The ML/Bayesian linear Gaussian model
-
Maximum likelihood and Bayesian estimation
-
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 see the Booklist for Part IIA Courses for references for this module.
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
D4
Ability to generate an innovative design for products, systems, components or processes to fulfil new needs.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 13/09/2018 15:53
Engineering Tripos Part IIA, 3F1: Signals & Systems, 2018-19
Module Leader
Lecturers
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Cover three basic topics in signals and systems which provide the basis for further topics in signal processing, communications, control and related subjects.
- Introduce the z-transform, which is the generalisation of the Laplace transform to discrete time systems.
- Introduce digital filtering.
- Introduce stochastic processes.
Objectives
As specific objectives, by the end of the course students should be able to:
- Be familiar with the theory and application of the z-transform.
- Analyse the stability of discrete-time systems
- Understand the use of correlation and spectral density functions.
- Analyse the behaviour of linear systems with random inputs.
Content
Enabling theory, application and design, Dr T. O’Leary and Dr F. Forni
Introduction to signals and systems, discrete time signals and systems, Z-transform (5L – O’Leary)
- Discrete signals and systems, LTI systems, convolution.
- z-transform and solution of linear difference equations
- System analysis in the z-domain.
- Impulse and frequency responses.
Applications & digital filtering (8L – Forni)
- Design and properties of digital feedback systems. Nyquist stability criterion.
- Design and properties of Digital Filters, FIR and IIR
- Analysis of systems with discrete/continuous interfaces.
- DTFT/DFT and links to z-transforms
- The Fast Fourier Transform (FFT)
- Windowed spectral analysis of data
- Introduction to 2D filtering, image analysis
Introduction to random processes and linear systems (3L – O’Leary)
- Continuous time random processes, correlation functions, spectral density.
- Response of continuous time linear systems to random excitation.
Coursework
Flight control
Learning objectives:
- Simulation of various aircraft models on the computer.
- Study real-time (manual) control and the limitations imposed by time delays.
- Design of a simple autopilot.
- Illustrate frequency response concepts in analogue and digital control systems, conditions for oscillation in feedback systems and stability.
- Gain familiarity with MATLAB.
Practical information:
-
Sessions will take place in the EIETL laboratory on Wednesdays and Fridays of full term from 11am-1pm.
-
Students will find it helpful to read through the lab sheet in advance of carrying out the experiment.
-
Students will have the option to submit a Full Technical Report.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 16/05/2018 13:31
Engineering Tripos Part IIA, 3F1: Signals & Systems, 2017-18
Module Leader
Lecturers
Lab Leader
Timing and Structure
Michaelmas term. 16 lectures.
Aims
The aims of the course are to:
- Cover three basic topics in signals and systems which provide the basis for further topics in signal processing, communications, control and related subjects.
- Introduce the z-transform, which is the generalisation of the Laplace transform to discrete time systems.
- Introduce digital filtering.
- Introduce stochastic processes.
Objectives
As specific objectives, by the end of the course students should be able to:
- Be familiar with the theory and application of the z-transform.
- Analyse the stability of discrete-time systems
- Understand the use of correlation and spectral density functions.
- Analyse the behaviour of linear systems with random inputs.
Content
Enabling theory, application and design, Dr T. O’Leary and Dr F. Forni
Introduction to signals and systems, discrete time signals and systems, Z-transform (5L – O’Leary)
- Discrete signals and systems, LTI systems, convolution.
- z-transform and solution of linear difference equations
- System analysis in the z-domain.
- Impulse and frequency responses.
Applications & digital filtering (8L – Forni)
- Design and properties of digital feedback systems. Nyquist stability criterion.
- Design and properties of Digital Filters, FIR and IIR
- Analysis of systems with discrete/continuous interfaces.
- DTFT/DFT and links to z-transforms
- The Fast Fourier Transform (FFT)
- Windowed spectral analysis of data
- Introduction to 2D filtering, image analysis
Introduction to random processes and linear systems (3L – O’Leary)
- Continuous time random processes, correlation functions, spectral density.
- Response of continuous time linear systems to random excitation.
Coursework
Flight control
Learning objectives:
- Simulation of various aircraft models on the computer.
- Study real-time (manual) control and the limitations imposed by time delays.
- Design of a simple autopilot.
- Illustrate frequency response concepts in analogue and digital control systems, conditions for oscillation in feedback systems and stability.
- Gain familiarity with MATLAB.
Practical information:
-
Sessions will take place in the EIETL laboratory on Wednesdays and Fridays of full term from 11am-1pm.
-
Students will find it helpful to read through the lab sheet in advance of carrying out the experiment.
-
Students will have the option to submit a Full Technical Report.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
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.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 22/09/2017 18:35
Pages
