Uppsala universitet
Statistical Aspects of the Split Spectrum Technique

Mats G. Gustafsson

PhD Thesis, Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 106. Uppsala 1995, ISBN 91-554-3490-8.


Abstract:
A practical well established signal processing technique for suppression of ultrasonic clutter known as split spectrum processing (SSP) is studied in an attempt to obtain better theoretical understanding and optimal parameter tuning.

The SSP technique relies on nonlinear processing of the outputs from a filter bank which splits the received signal into different frequency bands. A general approach to parameter tuning of SSP is considered where an adaptive artificial neural network (ANN) replaces the nonlinear part of the SSP.

Extensions to an adaptive filter bank is also considered in the context of both a multilayer perceptron ANN operating on a delay line and the Wiener model of nonlinear dynamical systems. Both the ANN and the Wiener model are shown to have the same structure as the SSP and the potential of supervised learning of the ANN and system identification of the Wiener model is discussed.

Originating from the ANN approach, many theoretical aspects of how SSP works are presented. New insights about how SSP exploits phase and amplitude information is elaborated and conceptual links between the SSP filter bank and the short-time Fourier transform and other time-frequency methods such as wavelets are touched upon.

Employing a statistical pattern recognition perspective, the optimal detector for a known transient in additive Gaussian noise (the matched filter) is formulated as a time-frequency method and used for nonlinear clutter suppression. The new formulation is used to compare SSP with conventional detection theory and to obtain a unifying link with recent work on maximum likelihood amplitude estimation in the context of ultrasonics. It is also employed to show that the polarity thresholding SSP algorithm relies on a test statistic which is a nonlinear function of the observed samples.

A simple clutter model suitable for digital signal processing is developed based on physical principles. It is used mainly to motivate the theoretical studies of the optimal detectors in additive Gaussian noise and for evaluation of different algorithms.

As a final contribution, the underlying principle of SSP to produce and compound uncorrelated filter signals is reconsidered, resulting in a statistically based formula for the number of optimal filters to use and insights about the role of the filter bank in stationary as well as nonstationary noise. Other results include a new SSP algorithm based on a noncoherent detector for additive Gaussian noise which demonstrates that the original SSP filter bank can produce optimal statistics for in-phase noncoherent subband detection.

Keywords:
Keywords: ultrasonics, nondestructive evaluation, split spectrum, frequency diversity, flaw detection, clutter, statistical pattern recognition, artificial neural networks

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