Module Code: EEEM019 
Module Title: MATHEMATICS OF SIGNAL PROCESSING 

Module Provider: Electronic Engineering

Short Name: EEM.MSP

Level: M

Module Coordinator: ILLINGWORTH J Prof (Elec Eng)

Number of credits: 15

Number of ECTS credits: 7.5




Module Availability 
Autumn semester 


Assessment Pattern 
Unit(s) of Assessment

Weighting Towards Module Mark (%)

Written Closed Book Examination

80

Signal Analysis & Probability Assignments

20




Module Overview 



Prerequisites/Corequisites 
Students should have obtained an undergraduate degree in Electronic Engineering or a related technical subject e.g. physics or other engineering disciplines that work with classical "continuous" mathematics. In particular, students should have some background in arithmetic, complex numbers, integration and differentiation, trigonometry, and mathematical transforms 


Module Aims 
The aim of this module is to review, consolidate and extend the students knowledge of the underlying mathematical concepts and techniques of signal processing, including the mathematics of probability and random processes. It aims to provide the students with the analytical tools for solving basic signal processing problems. 


Learning Outcomes 
On successful completion, the students will have gained appreciation of the relevance of the statistical and deterministic signal processing methods to applications in communications, telematics, and related engineering areas. 


Module Content 
Random Processes, Lecturer JI Hours 10 lecture hours + 2 problem classes
[13] Probability  Interpretation of probability. Sample spaces and events. Axioms of probability. Joint and conditional probability. Bayes' formula. Independent events.
[46] The Random Variable  Discrete and continuous random variables. Distribution and density functions. Moments of a random variable. Gaussian random variables. Other continuous and discrete distributions.
[78] Jointly Distributed Random Variables  Joint, marginal, and conditional distributions. Bivariate distributions. Statistical independence. Covariance and correlation coefficient. Jointly Gaussian random variables.
[910] Random Processes  Probability distributions. Time and ensemble averages. Stationarity and ergodicity. Correlation functions. Power spectral densities of random signals. Wiener Khinchine theorem. Markov processes. Nonlinear and nonGaussian processes.
Signal Analysis, Lecturer SW Hours 9 lecture hours + 2 Problem Classes
[12] Signal Representation and Time Domain Analysis  Review of basic signal functions, Dirac Delta functions, Time scaling, shifting and reversal, linear and circular convolutions, auto and cross correlations, properties of correlation, signal power/energy.
[34] Frequency Domain Analysis  Continuous time Fourier Transform, Properties of Fourier Transforms, Parseval’s Theorem, Frequency selective filtering, Sampling theory and practical limitations (Nyquist rate), Quantisation.
[59] Discrete Signal Transforms  Discrete Fourier Transform, Fast Fourier Transform, zTransform, ROC, Properties of zTransforms, Inverse zTransforms.
Digital Signals and Systems, Lecturer SW Hours 9 Lecture hours + 2 Problem Classes
[13] General Digital System Properties  Causality, Conditions of causality, Real systems, Stability, Conditions of stability, Polezero representations of Digital Systems, System Frequency Response, General Difference Equation, Transfer Function, Phase response, Magnitude response, Relationship between Impulse response and Frequency response.
[45] Filter Design  Discrete Linear Time Invariant Systems, Forms of implementation of a Discrete filter, Digital filter design criteria, Impulse Invariant Method.
[67] Bilinear Transformation with Butterworth and Chebyshev LowPass Filter.
[89] Finite Impulse Response (FIR) Filters  Practical FIR filter implementation, Relationship between Low and High pass FIR filters, Bandpass and Bandstop FIR filter design, Hamming and Hann windows for FIR filter design.



Methods of Teaching/Learning 
Lectures: 30 hours over 10 weeks



Selected Texts/Journals 
G. James, Advanced Modern Engineering Mathematics, Prentice Hall Publishing 0130454257 B
A.Croft, R. Davison, M. Hargreaves, Engineering Mathematics: 3rd ed, Prentice Hall Publishing 0130268585 B
H. Baher, Analog & Digital Processing: 2nd ed, John Wiley Publishing 0471623547 B
S.L. Miller & D.G. Childers, Probability and Random Processes (with applications to Signal Processing and Communications), Elsevier Academic Press 0121726517, (£58 as of July 2007)



Last Updated 
15th June 2010 


