Undergraduate Teaching 2017-18

Engineering Tripos Part IIB, 4F7: Statistical Signal Analysis, 2017-18

Engineering Tripos Part IIB, 4F7: Statistical Signal Analysis, 2017-18

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Module Leader

Dr S.S. Singh


Dr S.S. Singh

Timing and Structure

Lent term. 16 lectures (including examples classes). Assessment: 100% exam


3F3; Useful 3F1 and 3F8


The aims of the course are to:

  • Continue the study of statistical signal processing from the basics studied in 3F3.
  • Introduce the fundamental concepts and methods of adaptive filtering.
  • Introduce time-series models, in particular Hidden Markov Models; understand their role in applications of signal processing; develop techniques for estimating hidden signals from noisy observations.
  • Develop techniques for calibrating statistical time-series models for real data.


As specific objectives, by the end of the course students should be able to:

  • Understand the theory and objectives of optimal filtering in an adaptive setting.
  • Recognise and describe the classes of problem where adaptive filtering might be applied.
  • Describe the implementation of the Least Mean Square and its variants, and understand their convergence properties.
  • Understand the basic principles of Kalman filtering and filtering for hidden Markov models.
  • Understand the principles of Sequential Importance Sampling with Resampling, aslo known as particle filtering, for inference in hidden Markov models.
  • Undertand Maximum Likelihood estimation for model calibration and its implementation.
  • Formulate signal processing tasks in a model-based framework, and to estimate the model parameters.


This course is about fitting statistical models to data that arrives sequentially over time. Once an appropriate model has been fit, tasks like predicting future trends or estimating quantities not directly observed can be performed.  The statistical modelling and computational methodology covered by this course is widely used in many applied areas. For example, data that arrives sequentially over time is a common occurrence in Signal Processing (Engineering), Finance, Machine Learning, Environmental statistics etc.
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the ARMA model (studied in 3F3.) However,  this course will look at more versatile models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim to describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process. 


  • Optimal linear filtering: the least mean square algorithm and its variants; recursive least squares; exemplar problems in signal processing.
  • Introduction to state-space models and the recursive optimal linear filtering; the Kalman filter.
  • Introduction to hidden Markov models: definition; inference aims; exact computation of the filter.
  • Importance sampling: introduction; weight degeneracy.
  • Sequential importance sampling and resampling (also known as the particle filter): application to hidden Markov models; filtering; smoothing.
  • Calibrating hidden Markov models: maximum likelihood estimation and its implementation
  • Exemplar problems in Signal Processing
  • Examples Papers


Please see the Booklist for Group F Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.


The UK Standard for Professional Engineering Competence (UK-SPEC) describes the requirements that have to be met in order to become a Chartered Engineer, and gives examples of ways of doing this.

UK-SPEC is published by the Engineering Council on behalf of the UK engineering profession. The standard has been developed, and is regularly updated, by panels representing professional engineering institutions, employers and engineering educators. Of particular relevance here is the 'Accreditation of Higher Education Programmes' (AHEP) document which sets out the standard for degree accreditation.

The Output Standards Matrices indicate where each of the Output Criteria as specified in the AHEP 3rd edition document is addressed within the Engineering and Manufacturing Engineering Triposes.

Last modified: 31/05/2018 13:01