Random Signal Analysis and Adaptive Filtering
This five-day intensive course imbeds a range of probabilistic concepts into a study of random discrete-time signals and presents a range of appropriate processing strategies, placing strong emphasis on digital filtering and adaptive schemes. Rather than explicitly building up the full probability underpinning usually seen in stochastic signal courses, the treatment here relies heavily on expectation as an operator similar to Fourier transformation and focuses on wide-sense stationary processes as interpreted in finite record-length scenarios. Thus the tasks familiar to DSP engineers - such as signal representation, transforming to the frequency and Z domains and convolution - are joined by ensemble averaging considerations. Wherever ergodicity can be applied, time-averaging also joins in the instrumentation armoury invoked.
The course primarily relies on the special Simulink Labkit DSP_Speedster for computer illustrations and activities, making use of specially-configured soft instruments for quick cementing of theory and practice. Secondarily, MATLAB code fragments and m-files are utilized as needed. Theoretical topics are necessarily carefully targeted to end applications, but nonetheless take on a broad sweep in doing so. Most treatment centres on Gaussian processes due to their prominent appearance in linear systems and their tractability for study of nonlinear processing.
Effects of filters, modulation and memoryless nonlinearity effects are characterized at raw signal level and also at a mean-equivalent level, where correlation allows randomness to be supplanted by deterministic equivalents. There is a premium on optimal processing strategies, especially as regards matched filtering, Wiener filters and real-time LMS adaptive filter behaviour.
All lecture sessions are immediately re-enforced by hands-on computer investigations. Three in-depth Laboratory Sessions are also included, affording opportunities for deeper confrontation of realistic engineering problems.
Who Should Attend?
The course is suitable for newcomers to the MATLAB/Simulink environment. Prior knowledge of probability concepts and notation, DSP and digital filters would be an advantage.
Course Content
One-dimensional random variables concepts underlying random signals. Stochastic signals and ergodicity. Gaussian processes, correlation matrices and white processes. Noisy sinusoids and properties of the Autocorrelation Function and Power Sprectral Density.
Measuring correlation and ensemble averaging. Linear Time-Invariant System effects on random signals. Bandlimited white noise, pink noise and colouration filtering equivalence.
Matched filters. Matched Filter Laboratory Session. The Orthogonality Principle and Wiener filtering. Matrix solutions for FIR Wiener filters. LMS adaptive filtering. LMS Filter Laboratory Session.
Zero-Memory NonLinearities for Probability Density Function control of computer-generated random signals. Mean-equivalence for ZMNL cross-correlations and Bussgang’s Theorem. Price’s Theorem for output autocorrelation. Shutterly’s expansion and bandwidth implications. Soft limiting and Baum’s tunable random process.
Transient signals plus noise. Modulation and other nonstationarities. Introduction to multi-rate random signals. Consolidation Design Laboratory Session.