Parseval Theory of Complex Wavelet Transform for Wavelet Family Including Rotational Parameters

摘要

A rotational parameter R_θ has been introduced to complex wavelet transform (CWT).The rotational CWT(RCWT) corresponds to a matrix element 〈ψ|U_2(θ;μ;k)|F〉 in the context of quantum mechanics,where U_2(θ;μ;k) is atwo-mode rotational displacing-squeezing operator in the 〈η| representation.Based on this,the Parseval theorem andthe inversion formula of RCWT have been proved.The concise proof not only manifestly shows the merit of Dirac'srepresentation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.