Wavelet transform implementation by layers

I.IntroductionWavelettheoryanditsapplicationhavebeendevelopedquicklyformallyyears,whichcoverquitealargeareaandprovideverygeneraltechniquesthatcanbeaPpliedtomanytasksinsignalprocessing,andhavenumerouspotelltialapplications.lnacousticresearchthereisatra-ditionofthefrequencyanalysisintermsofoctave,whichfitstheconceptof"constantQ"inwavelettransform,e.g.thepowerspectrumofmusicismeasuredintermsof1/3octave.Sofartheimplemelltationofwavelettransformha-sbeendevelopedonlyforoneoctave,e.g.themultiresolut…

Wavelet transform implementation by layers

A wavelet transform implementation by layers is developed for the non-one-octave case in the acoustic research. The scheme consists of two layers. The first layer is a typical subband coding method, which is computed octave by octave. The second layer is based on the continuous time wavelet series. The output of highpass in the subband coding becomes an input of the second layer, which consists of N pieces of 1/N octave filters. The discreted intervas of translation parameter in the second layer are unified, so the discretization is overcomplete and has some redundance. The reconstruction can be achieved in each stage, and finally the original signal can be reconstructed stage by stage from bottom to top. In this way the implementation of non-one-octave wavelet transform can be completed. The number of samples in the method is (N 1)/2-times of the subband coding method. When N=1, the method of non-one-octave wavelet transform decreases to the subband coding method.