Lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines | Zendy

Amir Averbuch | Zendy; А. Б. Певный | Zendy; Valery A. Zheludev | Zendy

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Lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines

Author(s) -

Amir Averbuch,

А. Б. Певный,

Valery A. Zheludev

Publication year - 2000

Publication title -

proceedings of spie, the international society for optical engineering/proceedings of spie

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.192

H-Index - 176

eISSN - 1996-756X

pISSN - 0277-786X

DOI - 10.1117/12.408645

Subject(s) - biorthogonal system , quadrature mirror filter , lifting scheme , mathematics , biorthogonal wavelet , discrete wavelet transform , linear phase , filter bank , wavelet , algorithm , prototype filter , quadrature (astronomy) , wavelet transform , filter (signal processing) , filter design , computer science , electronic engineering , artificial intelligence , computer vision , engineering

In the paper we present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction we used the interpolatory discrete splines which enabled us to design a library of perfect reconstruction filter banks. These filter banks are related to Butterworth filters. The construction is performed in a “lifting” manner. The dierence,from the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform (FFT). Two ways to choose the control filters are suggested. The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. These filters have linear phase property and the basic waveforms are symmetric. In addition, these filters yield perfect frequency resolution. Keywords: Discrete splines, biorthogonal wavelets, lifting scheme, Butterworth filters

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