EE4-13 Spectral Estimation and Adaptive Signal ProcessingLecturer(s): Prof Danilo Mandic
To provide students with in depth knowledge of the theoretical basis and applicability of conventional and modern methods for spectral estimation, and the algorithms which underlie adaptive signal processing.
To give students hands-on experience of using spectral estimation and adaptive signal processing techniques through structured MATLAB assignments based upon acoustic echo cancellation, high resolution frequency estimation applications in mobile communications and multichannel physiological recordings.
At the end of the course students should be able to:
Understand the fundamental statistical properties of signals. Perform dimensionality reduction in signal processing problems. Understand transform domain signal processing.
Describe the consequence of the term resolution as applied to a spectral estimator.
Derive and analyse the statistical properties of the conventional spectral estimators, namely the periodogram, averaged periodogram and Blackman-Tukey methods.
Formulate modern, parametric, spectral estimators based upon autoregressive (AR), moving average (MA), and autoregresive moving average (ARMA) models, and detail their statistical properties.
Discuss the fundamental role of order selection in parametric modelling. Apply data driven, empirical time-frequency-amplitude estimation techniques.
Derive the steepest descent, Least Mean Square (LMS), and Recursive Least Squares (RLS) adaptive filter algorithms and their understand their performance properties. Familiriase themselves with the concept of adaptive processing of nonstationary signals and Kalman filter.
Analyse the convergence of stochastic gradient algorithms. Understand the need for blind signal processing. Apply blind signal processing algorithms to separate independent sources. Analyse nonlinear and neural adaptive filters, based on the models of neurons within the brain.
Apply adaptive signal processing in mono- and stereophonic echo cancellation and equqalisation. Apply adaptive signal processing algorithms to the prediction of financial time series and biomedical problems such as ECG denoising and modelling of brain electrical signals for brain computer interfaces.
Aspects of estimation theory: bias, variance, maximum likelihood and efficiency. Resolution and stability; time-bandwidth product. Classical spectral estimation: periodogram, averaging and Blackman-Tukey method. Parametric models: linear, rational transfer function, and non-linear models. Order selection. Block and sequential parameter estimation techniques. Steepest descent, least mean square and recursive least squares adaptive algorithm families. Kalman filering. Blind equalization and source separation. Nonlinear adaptive filters and temporal neural networks. Time-frequency and time-scale methods. Spectral redundancy and cyclostationarity. Case studies.
One 3-hour exam in April/May
Coursework contribution: 0%
Closed or Open Book (end of year exam): Closed
Oral Exam Required (as final assessment): N/A
Prerequisite: None required
Course Homepage: unavailable