Selection of orthonormal transforms for improving the performance of the transform domain normalised LMS algorithm

Transform domain adaptive filters (TDAF) that employ orthonormal transforms to convert their input samples to a set of partially uncorrelated components, to be used as actual inputs to an adaptive linear combiner, are studied. A recently proposed performance index is used. The authors show that the efficiency of an orthonormal transform, in improving the performance of the LMS algorithm, depends on its ability to spread the energy levels of its output components. This gives a clear view of the filtering concept of the transformation process when it is thought of as a bank of parallel filters tuned to different portions of the spectrum of the input sequence. The filtering view is able to predict the performance of the TDAF and suggest transforms that suit specific applications