ENGINEERING TRIPOS PART IIA – 2012/2013

Module 3F1 – Signals and Systems

COURSES

1. Discrete Time Systems (Prof. K. Glover )
2. Random Processes (Prof N.G. Kingsbury)
3. Information Theory (Prof N.G. Kingsbury)

Cousework:

Flight control experiment. Laboratory report and/or full technical report.

AIMS

This course covers three basic topics in signals and systems which provide the basis for further topics in signal processing, communications, control and related subjects. The first topic introduces the z-transform, which is the generalisation of the Laplace transform to discrete time systems. The second topic deals with stochastic processes. The third topic is an introduction to the theory of information in the context of transmission along a channel.

SYLLABUS

1. Discrete Time Systems (6L)

• Definition and properties of z-transforms.
• Convolution sum.
• Solution of difference equations.
• Stability.
• Impulse and frequency responses.
• Analysis of systems with discrete/continuous interfaces.
• Nyquist Stability Criterion

2. Random Processes (6L)

• Probability and Random variables.
• Random vectors.
• Ensembles and stochastic inputs.
• Stationary and ergodic processes.
• Correlation functions.
• Spectral density.
• Response of linear systems to stochastic inputs.

3. Information Theory (4L)

• Information and Entropy.
• Channel capacity.
• Coding.

OBJECTIVES

On completion of the course a student should:

• Be familiar with the theory and application of the z-transform.
• Be able to analyse the stability of discrete-time systems
• Understand the use of correlation and spectral density functions.
• Be able to analyse the behaviour of linear systems with random inputs.
• Be familiar with the key concepts of information Theory, such as how much information is conveyed by a given message, and be able to calculate the entropy of source data with known statistics.

ASSESSMENT

By examination

REFERENCES

Please see the Booklist for Part IIA Courses for references for this module.