Engineering and the Environment, University of Southampton

Knowledge and understanding
Having successfully completed the module, students will be able to demonstrate knowledge and understanding of:

• Concepts fundamental to signal modelling, signal generation and signal classification.
• The similarities and differences between continuous and discrete signals.
• The rationale for and interpretation of Fourier analysis.
• The methods used to describe random signals.
• The effects of filters.

Cognitive (thinking) skills
Having successfully completed the module, you will be able to:

• Appreciate the significance and importance of time series data.
• Interpret information contained in time histories through transformation (Fourier) methods.

Practical, subject specific skills
Having successfully completed the module, you will be able to:

• Understand and recognise the various classes of signals.
• Understand the need for both time and frequency domain descriptions of data and to decide which description is most appropriate for a particular application.
• Interpret results taking due account of the several sources of error that arise and to quantify those errors.
• Have a practical understanding of single-channel and dual-channel frequency domain concepts such as a frequency spectrum, spectral density, cross-spectrum and coherence.

Key transferable skills
Having successfully completed the module, you will be able to:

• Use Fourier transform methods for all classes of data in any application.

The aims of this module are to:

• Introduce the concepts that are basic to the acquisition, analysis and interpretation of time histories.
• Ensure that students acquire an appreciation of the generic nature of signal processing and the relevance and applicability of the methodology to engineering and many other fields.
• Ensure that students develop sufficient mathematical expertise to underpin the study of signal processing.

• Students new to this topic very often find it 'difficult', 'confusing' and very soon get lost in new terminology, unfamiliar concepts and the need to use mathematical language and methods. The most important outcome of this course is that students should be able to distinguish between conceptual ideas and principles and the mathematical language. This will lead to being able to see the wide relevance of the subject and confidence in being able to tackle data analysis problems systematically.

• Time histories and their classification.
• Deterministic signals, periodic signals and Fourier series, almost periodic signals, transients and the Fourier integral. Amplitude, phase, energy and power spectra.
• Convolution and the effect of linear filters, time and frequency domain considerations, impulse response functions, transfer functions and frequency response functions, system identification. Data windowing and resolution.
• Uniform sampling of continuous time histories. Fourier transforms of sampled data, aliasing and anti-aliasing filters. The discrete Fourier transform and the fast Fourier transform algorithm.
• Random signals, the concepts of probability, expectation and moments. Stationary and nonstationary processes. Auto- and cross-correlation (covariance) functions: auto (power) and cross spectra. Linear system input-output relationships in the time and frequency domains.
• System identification using estimators H1, H2 and H3. The coherence function and its interpretation.
• Estimators for stochastic processes; bias and variability errors and confidence intervals. Spectral estimators, raw and smoothed spectra. Transfer function and coherence function estimators and their properties.

2 lectures/week.

3 laboratory classes, the first of which is not assessed. Feedback on laboratory reports will be given within two weeks of the submission deadline.

Examples are provided to students in order to practice their analytical skills and these are backed up with interactive tutorial sessions. Students are encouraged to read supporting texts and a booklist is provided.

Secondary text

Random Data
2nd Edition, 1986, J S Bendat
A G Pierson, John Wiley
0471040002

Applied Time Series Analysis, 1978, R K Otnes
L Enochson, John Wiley
047124357

Spectral Analysis and its Application, 1968, G M Jenkins
D G Watts, Holden Day
081624642

Spectral Analysis and Time Series, 1981
Volume 1
Volume 2, M B Priestley, Academic Press
0125649010
0125649029