Statistical Signal Processing (P01824)

? Credit Points : 20 ? SCQF Level : 11 ? Acronym : EEL-P-PGSSP

This course introduces the fundamental statistical tools that are required to analyse and described advanced signal processing algorithms. It provides a unified mathematical framework in which to describe random events and signals, and how to describe key characteristics of random processes. It investigates the affect of systems and transformations on time-series, and how they can be used to help design powerful signal processing algorithms. Finally, the course deals with the notion of representing signals using parametric models; it covers the broad topic of statistical estimation theory, which is required for determining optimal model parameters. Emphasis is placed on relating these concepts to state-of-the art applications and signals. This module provides the fundamental knowledge required for the advanced signal, image, and communication courses in the M.Sc. course.

? Keywords : Probability, scalar and multiple random variables, stochastic processes, power spectral densities, linear systems theory, linear signal models, and estimation theory.

Entry Requirements

? Pre-requisites : It is strongly recommended that the student has previously attended an undergraduate level course in signals and systems, or digital signal processing.

Subject Areas

Home subject area

Postgraduate (School of Engineering and Electronics), (School of Engineering and Electronics, Schedule M)

Delivery Information

? Normal year taken : Postgraduate

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 5 hour(s) per week for 10 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	12:00	KB
Lecture	Thursday	09:00	10:50	KB

Summary of Intended Learning Outcomes

At the end of this module, a student should be able to: define, understand and manipulate scalar and multiple random variables, using the theory of probability; explain the notion of characterising random variables using moments, and be able to manipulate them; explain, describe, and understand the notion of a random process and statistical time series; characterise random processes in terms of its statistical properties, including the notion of stationarity and ergodiciy; define, describe, and understand the notion of the power spectral density of stationary random processes; analyse and manipulate power spectral densities; analyse in both time and frequency the affect of transformations and linear systems on random processes, both in terms of the density functions, and statistical moments; explain the notion of parametric signal models, and describe common regression-based signal models in terms of its statistical characteristics, and in terms of its affect on random signals; discuss the principles of estimation theory, define basic properties of estimators, and be able to analyse and calculate the properties of a given estimator; apply least squares, maximum-likelihood, and Bayesian estimators to model based signal processing problems.