On the Zeros of Daubechies Orthogonal and Biorthogonal Wavelets

Abstract

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets <i>Bior</i>3.5, <i>Bior</i>3.9 and <i>Bior</i>6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets <i>db</i>6 and <i>db</i>8

Wavelet packet transform-based compression for teleoperation

“…40 Mathematically, the form of the corresponding mother and scaling functions 41 for Bior wavelet family can be given as…”

“…The biorthogonal wavelet family differs from the function side since they are not based on vanishing moments. 40 Mathematically, the form of the corresponding mother and scaling functions 41 for Bior wavelet family can be given as…”