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Unit information: Optimum Signal Processing in 2016/17

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Unit name Optimum Signal Processing
Unit code EENGM1000
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Achim
Open unit status Not open




School/department Department of Electrical & Electronic Engineering
Faculty Faculty of Engineering


The aim of this module is to bridge the gap between classical and modern methods of signal analysis, with an emphasis on the processing of stochastic signals. Students will gain an awareness of optimum signal processing methods primarily based on the least squares error criterion. Optimum filter design will be presented, based on the Wiener filter followed by LMS and RLS filter realizations. Three key application uses of this technology are spectrum estimation, noise cancellation and beamforming. These will be covered from a theoretical and application perspective. An introduction to advanced parameter estimation techniques will also be presented.


  • Introduction; signal classes, stochastic processes, scope, tools, application areas
  • Matrix methods and Numerical Linear Algebra; definitions, operations, solution of equations
  • Stochastic processes and Parameter Estimation; stationarity, statistics, distributions, orthogonality, introduction to parameter estimation (MMSE, ML, MAP)
  • Optimum Least-Squares Filtering; normal equations, Wiener filtering, AR, MA, ARMA models, linear prediction, lattice filters, Kalman filters
  • Adaptive Digital Filters; structure and configurations, performance criteria, error surface searching, gradient methods, LMS, RLS, convergence, fast algorithms and numerical stability
  • Model Selection and Parameter Estimation; least squares, Bayesian, maximum likelihood
  • Spectral Estimation; DFT, FFT (periodogram), model based techniques (MA, AR, ARMA)
  • Adaptive Noise Cancelling; reference signal, output SNR, leakage, applications
  • Adaptive Beamforming; conventional methods, adaptive methods, constrained and unconstrained methods, direction of arrival estimation

Intended learning outcomes

On completing this unit, the student will be able to:

  1. Quantify the limitations of conventional methods of spectrum estimation.
  2. Implement superior model-based algorithms.
  3. Design and realise optimum code adaptive digital filters for a range of application scenarios including noise cancellation, linear prediction and beamforming.

Teaching details


Assessment Details

Exam, 2 hours, 100% (All ILOs)

Reading and References

Hayes, M.H., Statistical Digital Signal Processing and Modeling, New York : Wiley, ISBN:0 4715 9431 8 (TK5102.9 HAY)

Kay, S., Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice Hall, ISBN:0 1334 5711 7

Clarkson, Optimum and Adaptive Signal Processing, CRC Press, 1993, ISBN:0 8493 8609 8 (TK 5142.5 CLA)

Haykin, S., Modern Filters, Macmillan, 1989, ISBN:0 0235 2750 1 (TK 7872.FSHAY)