A larger class of wavepacket eigenfunction systems which contains Cauchy wavelets and coherent states

A larger class of systems of almost localized wavepackets is proposed. This class contains the Cauchy wavelet system and the coherent state system as special cases. The wavepacket systems in this class are the eigenfunction systems of a kind of linear operators, and they are invariant under the time-shift. Moreover, we show that they are `pseudoorthogonal´ over-complete systems in L². An application of them to the diagonalization problem of the autocorrelation functions of stochastic processes via overcomplete wavepacket systems is also proposed