ENGINEERING TRIPOS PART IIA - 2012/2013

Project SF1 - Data Analysis

Leader: Prof W J Fitzgerald email: wjf1000

Project Type: Standard
Project Category:
Prerequisites: None
Timing: Fridays 9-11am, Tuesdays 11-1pm

SUMMARY

This project will start by consolidating on some of the concepts introduced in the second year concerning Fourier transforms and the DFT. Several data series will be studied using these methods and the spectral content of the signals will be analysed. The effect of various data windows applied to the data will be investigated. Filters with various frequency responses will be designed and applied to various data sets. Alternative forms of spectral estimators will be studied. Parametric models and the methods of parameter estimation and model selection will be investigated (Least squares, maximum Likelihood and Bayesian methods). Inverse problems and deconvolution using various approaches will be introduced and used to identify signals that have been distorted by the measurement process. The stability of these methods in the presence of additive measurement noise will be investigated.

All of these methods are applicable to general fields of science and engineering and hopefully the project will prove useful for students hoping to specialise in different areas.

AIMS

• To introduce some of the standard approaches to Data Analysis and apply them to various real data sets (acoustic, biomedical, geophysical etc).
• To develop alternative approaches which in certain situations can yield much better performance.
• To introduce parameter estimation and deconvolution techniques.

FORMAT

Students will work in pairs.

ACTIVITIES

Week 1: Spectral analysis of the data sets using the DFT with data windows.

Week 2: Design and data filtering. Alternative approaches to spectral estimation (Parametric Approach).

Weeks 3 & 4: Implementation of Parameter estimation methods and applications to the given data sets. Investigation of Inverse methods.

MINI-LECTURES

Three mini-lectures will be presented:

1. Revision of Fourier methods;
2. Filter design and Spectral estimation methods;
3. Parameter estimation and Deconvolution.

Data to be Analysed

1. Several Geophysical time series having many (known) spectral components will be studied.
2. Various Biomedical data records (EEG) taken under different conditions will be investigated.
3. Data containing Change-points (d.c. step changes, ramps, AR models etc) will be studied and various parameters will be estimated.
4. An example of an optical system (diffraction will be used to demonstrate some deconvolution methods in the spatial domain. The data will be simulated under various noise conditions.

Methods to be Employed

1. Fourier transforms, the DFT and introduction to the FFT
2. Digital filter design (FIR and IIR), Data smoothing methods (Savitzky-Golay filters). Autoregressive spectral analysis
3. Estimation of Parameters using Least Squares, Maximum Likelihood and Bayesian approaches.
4. Inverse methods; Maximum Entropy and Regularisation methods.

ASSESSMENT

Format: Submission Date - Marks

Interim report 1: Thursday 16 May 2013 - 15 marks

Interim report 2: Thursday 23 May 2013 - 15 marks

Final report: 4pm Friday 7 June 2013 - 50 marks

Last updated: November 2012