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

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2008,（9）
• 页码范围: 598-602
• 页数: 5页
• 语种: 英文

摘要

A rotational parameter Ro has been introduced to complex wavelet transform (CWT).The rotational CWT (RCWT) corresponds to a matrix element <ψ|U2(θ;μ;k)|F> in the context of quantum mechanics,where U2(θ;μ;k) is a two-mode rotational displacing-squeezing operator in the <η| representation.Based on this,the Parseval theorem and the inversion formula of RCWT have been proved.The concise proof not only manifestly shows the merit of Dirac's representation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.