Adaptive harmonic wavelet transform with applications in vibration analysis

An adaptive harmonic wavelet transform is developed by taking advantage of the flexibility of the generalized harmonic wavelets. It first constructs a partition tree, which contains a great number of disjoint partitions of the frequency axis of a signal with each corresponding to an orthogonal harmonic wavelet basis. Then it searches the tree for the partition to represent the signal most sparsely. Since the corresponding basis is adapted to the composition of the signal, the transform can well reveal its characteristics. This is demonstrated with analysis examples of some simulated and vibration signals as well as comparisons with the conventional orthogonal harmonic wavelet transforms and wavelet packet transform.