Optimal model for 4-band biorthogonal wavelets bases for fast calculation

Abstract

A class of 4-band symmetric biorthogonal wavelet bases has been constructed, in which any wavelet system the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters. Thus, the least restrictive conditions are needed for forming a wavelet so that the free degrees can be reversed for application requirement. Some concrete examples with high vanishing moments are also given, the properties of the transformation matrix are studied and the optimal model is constructed. These wavelets can process the boundary conveniently, and they lead to highly efficient computations in applications.

The bounds estimate of sub-band operators for multi-band wavelets

“…A so-called d -circular matrix [ 20 ], which is generated by the filters , is denoted as . For , is as follows: …”

“…In [ 20 ], a 4-band symmetric biorthogonal wavelets which is denoted as Op(12-12) is designed. The corresponding wavelet filter banks are as follows: where , , , , , , , , , , , .…”

“…It has been shown that the eigenvalues of appear in pairs of reciprocal, and have the same eigenvalues [ 20 ]. It is obvious that .…”

A new modified wavelet-based ECG denoising

“…The Symlet wavelet obtains the symmetry by reducing the vanishing moment [12]. In recent years, some scholars have proposed some optimized methods to construct wavelets for specific applications [13][14][15][16][17]. In [13], a class of 4-band symmetric biorthogonal wavelet bases is constructed.…”

“…In recent years, some scholars have proposed some optimized methods to construct wavelets for specific applications [13][14][15][16][17]. In [13], a class of 4-band symmetric biorthogonal wavelet bases is constructed. They proposed that the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters in any wavelet system.…”