ADAPTIVE ORTHOGONAL HARMONIC WAVELET TRANSFORM AND APPLICATIONS

摘要

This paper develops an adaptive orthogonal harmonic wavelet transform by exploiting thernflexibility of the generalized harmonic wavelets. It addresses the problem of how to choose anrnorthogonal set of harmonic wavelets to ‘best' represent a given signal. We first introduce arnconcept of partition tree. It provides numerous choices to partition the frequency axis of arnsignal and each of the partitions corresponds to an orthogonal harmonic wavelet basis. Thenrnwe present an algorithm to search the tree for the partition and basis to represent the signalrnmost sparsely. Since the selected basis is adapted to the composition of the signal, therntransform can well reveal its characteristics. This is shown by simulated and vibration analysisrnexamples.