Autumn semester

Unit(s) of Assessment	Weighting Towards Module Mark (%)
Written Closed Book Examination	80
Signal Analysis & Probability Assignments	20

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

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.

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.

Random Processes, Lecturer JI
Hours 10 lecture hours + 2 problem classes

[1-3] Probability - Interpretation of probability. Sample spaces and events. Axioms of probability. Joint and conditional probability. Bayes' formula. Independent events.

[4-6] 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.

[7-8] Jointly Distributed Random Variables - Joint, marginal, and conditional distributions. Bivariate distributions. Statistical independence. Covariance and correlation coefficient. Jointly Gaussian random variables.

[9-10] 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 non-Gaussian processes.



Signal Analysis, Lecturer SW
Hours 9 lecture hours + 2 Problem Classes

[1-2] 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.

[3-4] 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.

[5-9] Discrete Signal Transforms - Discrete Fourier Transform, Fast Fourier Transform, z-Transform, ROC, Properties of z-Transforms, Inverse z-Transforms.

Digital Signals and Systems, Lecturer SW
Hours 9 Lecture hours + 2 Problem Classes

[1-3] General Digital System Properties - Causality, Conditions of causality, Real systems, Stability, Conditions of stability, Pole-zero representations of Digital Systems, System Frequency Response, General Difference Equation, Transfer Function, Phase response, Magnitude response, Relationship between Impulse response and Frequency response.

[4-5] Filter Design - Discrete Linear Time Invariant Systems, Forms of implementation of a Discrete filter, Digital filter design criteria, Impulse Invariant Method.

[6-7] Bilinear Transformation with Butterworth and Chebyshev Low-Pass Filter.

[8-9] 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.

Lectures: 30 hours over 10 weeks 

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 0-12-172651-7, (£58 as of July 2007)

15th June 2010