General formula for finding mother wavelets by virtue of Dirac's representation theory and the coherent state

摘要

The admissibility condition of a mother wavelet is explored in the context of quantum optics theory. By virtue of Dirac's representation theory and the coherent state property we derive a general formula for finding qualified mother wavelets. A comparison between a wavelet transform computed with the newly found mother wavelet and one computed with a Mexican hat wavelet is presented.