ENGINEERING TRIPOS PART IIB – 2012/2013

Module 4F7 - Digital Filters and Spectrum Estimation

AIMS

This module continues the study of digital signal processing (DSP) systems, continuing from the basics studied in 3F1/3F3. The first aim of the course is to introduce the fundamental concepts and methods of adaptive filtering, i.e. filters which attempt to adapt their parameters automatically on-line to the data at hand - good examples of this are echo cancellation in telephony or background noise cancellation for aircraft pilots. Modern filtering theory will be introduced for state-space models (i.e. the Kalman filter) and for Hidden Markov Models. This part of the course is an extension of the basic filter design material combined with the optimal filtering material from 3F3. In the second part of the course optimal spectrum estimation is studied. The aims are to develop the basic techniques for estimating the power spectrum of a random signal, i.e. what is the average frequency content of a signal, based just on a set of measured signal values. The course introduces both non-parametric (Fourier transform-based) and parametric model-based methods for this.

LECTURE SYLLABUS

Adaptive Filters (8L, Dr S.S. Singh)

• Optimal linear Filter: Wiener Filter
• LMS Algorithm and its variants
• Adaptive Filtering without Reference Signal
• RLS Algorithm
• State-space models and the Kalman filter
• Hidden Markov Models
• Applications

Spectral estimation (8L, Dr S.S. Singh)

• Non-Parametric Methods: Data Windows; Frequency resolution; Correlogram; Periodogram; Bartlett; Blackman-Tukey; Welch methods
• Parametric Methods; Autogressive Moving Average (ARMA) models; Sinusoidal Models; Yule-Walker Equations; Least Squares; Maximum Likelihood;

Lectures will be supported by interactive computer demonstrations using MATLAB.

OBJECTIVES

On completion of the module students should:

• Understand the theory and objectives of optimal (Wiener) filtering in an adaptive setting
• Be able to recognise and describe the classes of problem where adaptive filtering might be applied;
• Be able to describe the implementation of the LMS and RLS adaptation algorithms, and understand the their convergence properties. Understand the basic principles of Kalman filtering and filtering for Hidden Markov Models;
• Understand the principles of spectrum estimation, windowing, resolution;
• Understand and be able to apply non-parametric spectral analysis methods;
• Be able to specify data requirements in order to achieve specified spectral analysis criteria;
• Be able to formulate signal processing tasks in a model-based framework, and to estimate the model parameters

REFERENCES

Please see the Booklist for Group F Courses for references for this module.

Last updated: June 2012