Aims & Learning Objectives:
Aims: To introduce students to algorithms and techniques for processing random signals, together with the hardware for their practical realisation.
Objectives:
At the end of this unit students should be able to: (i) explain the concepts of ensemble average, statistical stationarity, wide-sense stationarity and ergodicity, (ii) interpret autocorrelation and cross-correlation functions and utilise these to explain the operation of linear systems excited by wide-sense stationary random signals, (iii) use auto and cross power spectral densities in typical instrumentation applications, (iv) use the averaged periodogram spectrum estimation techniques, (v) design the coefficients of a minimum mean squared error based linear predictor, (vi) derive the Wiener filter, (vii) develop the LMS algorithm from the method of steepest descent, (viii) apply adaptive signal processing in noise cancellation, equalisation and acoustic echo cancellation for handsfree communications, (viii) describe the key issues involved in the selection of a DSP configuration.
Content:
Random signals: amplitude properties, cdf, pdf, variance and general moments, stationarity, ergodicity and independence. Auto and cross correlation functions, effect of linear systems, auto and cross power spectral densities, role in system identification. Spectral estimation: bias-variance trade-off, periodogram, averaged periodogram estimators, application to spectrum analyser. Adaptive signal processing: Wiener filtering, method of steepest descent, LMS algorithm, properties, applications, RLS family. DSP architectures: DSP devices, precision, structures and performance.
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