Module Overview

Differential equations

Review of solving Differential Equations using the Laplace transform and the definition of a transfer function. Modelling with differential equations and the application of the Laplace Transform in the derivation of the input/output relationship for Linear systems.The use and definition of poles and zeros in the transform domain. The analysis of engineering systems and their representation by the Block Diagram.

Discrete Transforms

The definition of the Z-transform and the z transform of simple discrete functions. Analytical calculation of the z-transform of simple functions, including the single pulse. The link between the Z- and Laplace transforms in the s-plane. The discrete Fourier transform and its inverse. Analytical calculation of the DFT of simple functions, including the single pulse. The relation of the DFT to the Fourier transform. Matrix representation of the DFT. Convolutions and correlation of discrete sequences including circular convolution and cross-correlation.

Discrete Systems

The mathematical definition of sampling a continuous signal. Discrete systems, difference equations and their role in engineering systems analysis. The solution of difference equations by substitution and characterising their behaviour.

Applications of the discrete transforms

The discrete transforms and their use in solving difference equations. The sample of the transform of a continuous signal and the Discrete transform of the sampled signal. Modelling engineering systems as discrete systems and interpreting the behaviour of solutions. Characterisation of poles and zeros in the solution of difference/differential equations. Impulse response and transfer functions for discrete systems.

Module Content & Assessment
Assessment Breakdown	%
Other Assessment(s)	30
Formal Examination	70